Question
Consider three concentric shells of metal A, B and C are having radii a, b and c respectively as shown in the figure
Their surface charge densities are
respectively. Calculate the electric potential on the surface of shell A
![](data:image/png;base64,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)
The correct answer is: ![fraction numerator sigma over denominator epsilon subscript 0 end subscript end fraction open parentheses a minus b plus c close parentheses](data:image/png;base64,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)
The electric potential on the surface of shell
![V subscript A end subscript equals fraction numerator 1 over denominator 4 pi epsilon subscript 0 end subscript end fraction. fraction numerator q subscript a end subscript over denominator a end fraction plus fraction numerator 1 over denominator 4 pi epsilon subscript 0 end subscript end fraction plus fraction numerator q subscript b end subscript over denominator b end fraction plus fraction numerator 1 over denominator 4 pi epsilon subscript 0 end subscript end fraction. fraction numerator q subscript c end subscript over denominator c end fraction](data:image/png;base64,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)
Or ![V subscript A end subscript equals fraction numerator 1 over denominator 4 pi epsilon subscript 0 end subscript end fraction. fraction numerator 4 pi a to the power of 2 end exponent sigma over denominator a end fraction plus fraction numerator 1 over denominator 4 pi epsilon subscript 0 end subscript end fraction. fraction numerator 4 pi b to the power of 2 end exponent open parentheses negative sigma close parentheses over denominator b end fraction plus fraction numerator 1 over denominator 4 pi epsilon subscript 0 end subscript end fraction. fraction numerator 4 pi c to the power of 2 end exponent sigma over denominator c end fraction](data:image/png;base64,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)
![open parentheses because q equals 4 pi r to the power of 2 end exponent sigma close parentheses](data:image/png;base64,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)
![o r blank V subscript A end subscript equals fraction numerator sigma over denominator epsilon subscript 0 end subscript end fraction left parenthesis a minus b plus c right parenthesis](data:image/png;base64,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)
Related Questions to study
Work required to set up the four charge configuration (as shown in the figure) is
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAJgAAACkCAYAAABreuf3AAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAABJtSURBVHhe7Z17sE3lG8dfx92Ra3IO+SGJcimOEaKixhQml6F0MZpICekPlcgoQpOGiEw1pqZMSnIpxi1O1AxT7qnjEsf1uF9P7pf1W5/HWtpnn71pX959Dj2fmdfa691rb2ft97ue93mf93nXKuC4GEWxRJK3VRQrqMAUq6jAFKuowBSrxEVgq1atMhMnTvT2FOUf1IIpVlGB/Yf56aefzB133GEKFChgNm/eLFvq4knCBEYXygm0aNFCToLXf//9t/eukmhGjhxpWrZsaaZOnWoIhU6fPl3qGzVqJNu4QaA1Ujp27Ehw9prFp3nz5lKysrKc7Oxs+Tz7St6Qnp4u7cPWZ8KECVbaJCqBBbNy5Ur5A0MxYsQIORnE5YPAqFfsEnixU/w2qlmzprRBIIjLRptY7SL37t1rBg8ebNwTM6mpqVJHtzhz5kzTrFkz2VcSCyP+LVu2mJdfftmrudxOv/zyi5U2sSqwGTNmyLZ79+6yhSVLlsg27n29kgvXgOQoffr0MStWrJD3An//MWPGyNZGm1gV2OLFi41rek3JkiVlH+s1evToHHVKYqlTp45sXbdG2mPKlCmmWrVq1tokLgJLS0uTqyMYrghMLyaYMmvWLFOrVi3z6KOPekcoiebBBx80rv8lI8i3337bdOjQwaxZs8Zem7im0xo49jiU/De+g8nrwNGLkvfYbJOE5oMRzMOCZWdnaxeZT7DdJgkLtMKvv/6q/lc+Ah/svffeM24vY61NEiYwfLBhw4aZJk2aeDVKXvL999+bm266yUyePFnCFp06dfLeiTPSUVpmwIAB0s/7JVxQVrnx0Jx8xSpxF9jatWvNsWPHTEpKiqldu7ZXq/xXiYsPdubMGfPEE09IhkSrVq1Mly5dTIMGDUzBggXNW2+95R2l5BUbN2409evXN0WLFpU2Kly4sKlXr56ZP3++d4Q9YrZg27dvl4Dq008/bfr27SvD3aysLBn+rl+/Xk6iRIkSZvXq1aZMmTLep5REQQB8zpw5pn///pL7dfHiRWkXpuyI5hN4/fbbb02xYsW8T8SXmASG5apSpYr57rvvJPzAH4/ADh8+bHbu3Gk2bdokJ7NgwQJToUIFCVMoiYPeAxF98803Yr0ISxw5csTs2rXLZGRkyEX/ww8/mMaNG5vZs2d7n4ovBd0/Iuo+DKvVtGlT88ILL4jpTUpKku2lS5ekILizZ89K/fLly0VkTCsp9qFn6dWrl1m2bJlJTk4Wd4W2AWwKbXPhwgXpLull7rvvPpmTjDcx+WBkQT7//PPyx/JH+8KCQoUKidkl1lK6dGlTqVIlM2LECHlPsc+4ceNMu3btREC+oGgbREbbFC9eXNqlXLlypmLFiub111/3PhlfohYYo0V8qnPnzkm3yJYuky1Xhi86rhyEVr58eQm2coxiH9yWGjVqSLdIL0K7UM6fPy9tA/QsdJ233HKLWbdundTFm6gFhgnmj0M0hw4dktDEiRMnzMmTJ+WkTp06ZU6fPn1FcMDJceVwFWmxW/bs2SMX9759+8zRo0fFCPhtw5b28YXHcVg32jDeRC0wYlz8QVu3bhWHfv/+/eLcUzgh3jt+/PgV0XFCnAhWTYv9Qt4X2as7duwQI3DgwAExBDj5FNoHsdGj0E4YCxuj/JgEBuR7bdiwQUaMnAxi2717txSuHoR38OBBeV23bl35jGKfp556SgZWjCL//PNPs23bNmkbCqNIQklYOdqFcv/993ufjC8xhSk+/fRTcQ7bt29vqlatKk4j5hmzy9WBsLh6sHJ0qYsWLdLJ7gSBZWIdBAHvhg0bijNPPJJ6ehMsGiKjbRAc4SQbo8iYA60E6rhC7r33XnHk8bEQGN0ippirJDMz0/Ts2dOMHz/e+5SSCFh/2rZtWwmw4vAzosfXom1wZXxL9vHHH5tu3bp5n4ozCCwWXEfe6d27t+OOFJ3KlSs79erVc9LS0hz3hJyyZcs67kk5Q4cO9Y5WEo3bTTquJXNKlizppKSkOG5P41SoUMFJTk52XKvmzJs3zzvSDjELzIcTadmypeN2k1hEOak2bdo4GRkZ3hFKXoERGDt2rLRHkSJFnKZNmzqjRo1y3MGYd4Q94p5Nga/FggK6RSX/Ub16dZOenm7F3wpFTJF8RbkWMQmMech4341FubGIWmAE6lglPG3aNK9GUXITtcCwXK7DKLEtRQlH1AJbuHChxLuI2NuYw1JuDKIWmJ9uS3TYv6GGogQTlcD8OUZgMpv5SEUJRVQCw3qRSwSk4pCSqyihiEpgc+fOlclsH/XDlHBEJTAc/EC4r4HGw5RQRCwwUqVJyQmERLZg0SkKRCwwLFWovPpELOJUrj8iFhh3ZSGXOxjyitQPU4KJWGDhYl6sHFI/TAkmIoEhIBYHAAsEWF9XqlQp2SdLUgOuSjARCezHH38UIbGObtSoURIDY7FA69atxfEnfKEogUQkMHLsBw0aJFH8F198UerI9ebeEyxR11tjKsFEJLCPPvoo7O2YWC3EMilFCSRiJ19RIkEFplhFBaZYRQWmWEUFplhFBaZYRQWmWEUFplhFBaZYRQWmWEUFplhFBaZYRQWmWEUFplhFBaZYRQWmWEUFplhFBaZYRQWmWEUFplhFBaZYRQWmWEUFplhFBaZYRQWmWCUmgfG8yFdeecXbU5TcxCQwngGZqIcqKdcnUQls8+bN8jxotopyNSISGHeW7tSpk2nXrp0ZMWKEqVWrllgxRQlHRAKbNWuWmTlzplm9erWZMWOGmTBhgpk8ebJaMiUsEQns1ltvNQMGDLhyH7AqVarINjs7W7aKEkxEAuMB8EOHDjVTpkyRB40jNkW5GhEJjK6QJ9cfP37cLF261EydOtV7R1FCE5HABg4caDp27Gj69OljUlNTvVpFCU9EAitXrpw4+dxtmvvlf/3111KfkZEh+4oSTEQCe+2110yPHj3M+PHj5fbl+GPs02U+9thj3lGKEoATA0OGDHE2btzo7V0mMzPTqVatmren5DdoG9ooUURkwYIZPny4mTRpkrenKLmJSWCKci1UYIpVVGCKVVRgilVUYIpVVGCKVVRgilVUYIpVVGCKVVRgilVUYIpVVGCKVVRgilVUYIpVVGCKVVRgilVUYIpVVGCKVSISGMvW5s+f7+3lZN++faZXr17enqJcJmILxo1PHn74YVm6BidOnDBvvvmmqVmzplm4cKHUKYpPRAJ75JFHZGX34sWLTZcuXaSOtZHjxo2TO++0adNG6hTFJyKBNWnSxJw5c0ZeHzp0SLanT58WcZUuXdq0bt1a6hTFJyKBFStWzNSuXdvby8nFixfNPffc4+0pymUi9sHatm1rChUq5O39A+LT22kqwUQsMBx8//5ggXBrJ0UJJmKBIaSzZ896e5fhpihYNkUJJmKBAc5+IBcuXFALpoQkKoE9/vjjpmjRot6ekdCF+l9KKKISGPGwwoULe3tGb92khCUqgWGtGDWCxr+UqxGVwMD3uQi8qv+lhCNqgTFqxIphwcqUKePVKkpOYrJgWC/iYkA2xeeff26GDBlisrKyzKuvvirzlMeOHZP3lfwBbUaCQsLw7nQYFdyOcebMmc64ceOcUqVKOWlpaU6HDh2crl27Og0bNnTKlSsn9fPmzfM+oeQF/P5ly5Z1aG63t3EKFizolCxZ0hk6dKh3hD0K8M9lqUUOVgsL9r///c988MEHEuHnqR/UZ2Zmmq1bt5rffvvN/Pzzz+a5554zH374ofdJJRFgrVq0aCGveWhG1apVzcGDB822bdvM8uXLJeWqRIkSZsmSJdbCTDEJjLtNL1q0SJ5h5F4V5vz58+bkyZPmyJEj0k1yIhs3bpRnGyGyuXPn6oAggRAQJ3/vjTfeMJcuXTKnTp2SLJjdu3ebTZs2mT/++ENy+BAit6L3IwPxJGofbPv27eadd94Rq5SUlERXK9siRYrIVcFtzitUqGBSUlLkyqlRo4bp3LmznIxiHzKPz507J1nItAsGgLahlylfvrypXLmy9DyNGjWS29CTNGqDqAWG1apfv75JTk6Wq8MvpO0AGRecUPHixeWkEBtXULiUayW+4JL069dPLvzAgtgIkmOtaDuiALfffru4ODaIWmBfffWVPC+SZEOSDpkApyAwukoKguPKYVqJk+H1ypUrvW9QbLJ//37pObBOftvQJswb+0bANwBM9fF67dq1Uh9PohYYTjyCwWk8evSoCA0L5QuOrpDCiWGqERtXDg8yLVCggBbLhd/68OHD4g8jMr998JEpftsgOh/cnngTtcB4nB8i27Vrl4wafaH5hdEkJ+WfjH9CgwcPzmW2tcS/IByejrdz506xZjj3FARHHIxCG/ltAzZGklELjEUfv//+u9myZYuMFhk1Ug4cOCBXDoJj619FiA1wKhX78PDYZcuWmb/++utK+9A2iA2DwGvaiC3BcARpI+U9aoF16NBB/th169aJyIh5cbVg0RgGc0J79uy5ciK8pr/XMEViYIS/YsUK8asISWDNaCO6QdqH4gttx44dpn///t4n40tMcTBCFDxx7YEHHhCHkvAEfhmOJF2jb8k4GcQ3ffp0SfVREkOrVq1EWM2aNZPQBI48zY2P7McqcXMY8WPpbMTBYhIYNG/e3Kxfv17MK7Ev/khGKZwE/TwngdB47J+tobASGro+UqkIouJfkZRAmAKfCz+ZtilbtqwEwW1F8lF0zIwZM8ZJTk52XAvm3HzzzU5qaqpTunRpxxWbzH1NmzbNO1LJCz755BOZi3RHltJGtAulX79+jmsIvKPsELMF86FvJ3ti1apVYm4JwjZo0MB07dpVovlK3oNFwyfDWl3LYu3du1fiY6FWkEVC3ASm3FhMnDhR5jLT0tK8muiIehSpKP+GmATGCAVTSoyLrtGPdSn/Hfx2Rwe8DiaqLpIv69Onj9mwYYOpW7eu6dSpk+nWrZsMgZXrk2Bx4E/ffffd5s477/RqLi9PZAYHOP7JJ580FStWlDnp2267TeaZZ8yYIe/7RCww1Mp/RALb6NGjpQ6BQfCXK9cPfhv6YDwQD1kwPszCDBo0SMTF69mzZ8uSRV8TEyZMEMOTAwQWTHZ2tuOqMUehDjp27OjUrFnzyj40b97ccb/c21NuBGhP2j0Y2h3Z9OjRw6v5py7U8SEFxoF8ILD4QuO1q1zvSMfJysq68r5y4xBOYNTT3rS7D3qgLhQhnXzMnWupchTqFixYIO8HruT2u8VYh7PMm7377rvmpZde8mqU/Ai+GXpITU31aoysJqMuJJ7Q/hXul0jx2bRpU666f0tGRoYzduxYp2XLlk6hQoUk4s922LBh3hFKpBw9elRWCrGKKNYIPVaJ9g0GyQS6Q+np6eIyhXORIhLYl19+eaWLpPDliCvclwfijjydqVOnOp07d3bKly8vy9mKFi0q3+eX6tWre0cr0XLXXXfJ78rFWrt2bWfgwIHSTvEC3wtB8Z3oARHSduFcpIgEhjPnjh7lP/G/MNyXczWxZrJ3794iHObAEFWgoAIL70+aNMn7dN7C+VAC/YzrhTVr1sg8sP+7IjTmh9nSW9Br0HtEC4Ki/dEBvw+/E/9POCISWDDhvvyhhx6S+iJFilw50WuVpKSkkPXxLEzIXw1+PK5ORsUUPsNVer3RrFmzXOfuF34DLnRER2/y2WefOZmZmd4nI4fe62ouUkxzkSNHjgwZXMNh/+KLL2QFEQmITJhe6xYCJCMy98VSKltUqlRJ/uZw9OzZU5LzSF8BYkOuFeYKkn0fEvXq1Kkj6wzyI6Sm87exvRa0DTn8/P6cP2smIoGFvSQ05Ip/eUQdyWfFdvv27SXPa/jw4TlGFYGQe8QKYu6tP2fOHElwI2eMhQjBuCZcVhnnFUzwsozrmWeekX3ur/H+++/nEhg8++yz3qv8BxkTLHi+lsBY6YW4aA8yjRHJv804ZpqQRdd9+/aVAGv37t1DZl5EJTAaAsH48GP/25vQYckQHCuKsXAkvbGsjeREMi6XLl2a6xadiYSLx+02ZHEKTy8hHTyKnyhPYdqGCzkYXwCEnMh2ZdU3v3U0yYZYO7JifQgx+dNIOUBgeQmDAYbVJL/h/zRu3Nh7J/H4AUO2DGjwL/LBTxQRJBfiZ/F3k1TI63j5W9Fwff16lqFRAkMu15vACAW5VspJSUmROxwRFkq0oIKJycm/0cAfYY0BawfIY2fwgpPvWjR5wknILiCfwQAkP2UQa8JhAOnp6ZI9MGnSJON21eJXuENwWcxyPYgL8lt6ulowxSpqwRSrqMAUq6jAFKuowBSrqMAUixjzf1CiP2dNe9a8AAAAAElFTkSuQmCC)
Work required to set up the four charge configuration (as shown in the figure) is
![](data:image/png;base64,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)
The points resembling equal potentials are
![](data:image/png;base64,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)
The points resembling equal potentials are
![](data:image/png;base64,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)
In the following diagram the work done in moving a point charge from point P to point A, B and C is respectively as
then
![](data:image/png;base64,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)
In the following diagram the work done in moving a point charge from point P to point A, B and C is respectively as
then
![](data:image/png;base64,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)
Three charges
and
are placed at the vertices of an isosceles right angle triangle as in the figure. The net electrostatic potential energy is zero if
is equal to
![](data:image/png;base64,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)
Three charges
and
are placed at the vertices of an isosceles right angle triangle as in the figure. The net electrostatic potential energy is zero if
is equal to
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAASAAAAEPCAYAAADieRljAAAgAElEQVR4nO3d6VeUd5r/8fd9115FFcW+7yCLiiKICC7gEtNZptPpnJ4Hc6bP/C/zR8yzmTlnTuf0L326TTRqu4KiEMC0C7IYFxZZRWWvffk9sKnWjjFogBvuul7n5FGwuErhU9/7+m5KNBqNIoQQGlC1LkAIEb8kgIQQmpEAEkJoRgJICKEZCSAhhGYkgIQQmpEAEkJoRgJICKEZo9YFbKRgMIjH4yEQCGAymbDZbKiqSigUAsBgMGAymVAUReNKhYgPcRNAPp+P77//nsuXL/PgwQO2bdvGoUOHUBSF0dFRjEYjZWVlVFZWYrfbtS5XiLgQFwH05MkTenp66Onp4datW4yPj2MwGMjJyeHx48d8//335Ofnk5CQQFlZmdblChE3dB9AExMTfPXVV5w6dQqn00lLSwuFhYVkZWXx4sULTp06RX9/P/n5+WRmZmK1WrUuWYi4oesAmpyc5NSpU/zlL39henqaTz/9lM8//zw2yunu7mZhYQGPx0N2djbFxcWYzWaNqxYifmy5AIpEIrH/3sRgMGAwGADo6enh//7v/xgdHeXXv/41X3zxBUVFRbGvjUajGI1GEhISyMzMxO12b8h7EEK8tKUCKBAI8OTJE27dusXg4CA+n+9HX9Pc3ExTUxMLCwu0t7fT09NDWVkZH330EbW1tRiNL9/y7OwsU1NTqKpKdnY2GRkZqKqsShBiI22pAAoGgzx69Ii//OUvnDx58o0BpCgK1dXV3Llzh56eHhISEmhoaGDnzp2v9Xemp6e5d+8ewWCQkpIS0tLSNvKtCCHYYgsRo9Eofr+fubm5N4YPgN/vZ3l5me7ubh48eEBVVRWHDx/+UcCMj49z584dAoEApaWlpKambsRbEEK8YkuNgIxGI3l5eRw9epSEhASWl5d/9DV1dXU8f/6cO3fu4PP5qKurY8+ePa81lxcXFxkYGGBwcJDk5GSKiopITk7eyLcihGCLBZDZbKasrIyMjAw+/fTTNzaik5KSuHv3LlNTU1itVjIzM0lLS4v1d0KhEKOjo/T39/P06VMKCwvJy8vD6XRu9NsRIu5tqQBSVRWHw4HD4SArK+snv85isRAMBvH5fHi93tis2NLSEhMTE0xOTjI3N4ff7ycpKYn8/HwsFstGvQ0hxN9tqR7QamVnZ1NUVISqqty+fZtr164xPDzM6Ogo4+PjBINBrFYrTqeT1NRUUlNTZf+XEBrYUiOg1UpPT+fIkSOMj4/T09PDzMwMx48fZ+/evaSmphIOh7HZbGRnZ5OZmYnD4dC6ZCHiki4DKCEhgebmZnw+H+fPn2dhYYHl5WVsNhtpaWm8ePECVVUpKioiJydH1v8IoRFdBpCqqhQWFvLFF1/Q2NiIz+cjMTGRrKwslpeXGRkZYWlpifz8fHJycuTxSwiN6DKAAEwmE1lZWT9qVs/Pz3P79m3GxsbYtWsXOTk5GlUohNBtAP2UyclJ+vr68Hq9sR6QEEIbcdX8WFxc5O7du4yNjWG32ykuLiYhIUHrsoSIW7ofAYXDYSYmJhgeHqavr49vvvmGJ0+e4HA4uHnzJhkZGeTl5WldphBxSfcB5Pf7aW1t5X//938ZGxtjfHycSCTCo0eP+K//+i9sNhu///3vpREthAZ0H0CKomC320lNTcXhcFBdXY3FYiEUChEKhbDZbFqXKETcUqLRaFTrItZTJBJhfn6eubk5otFo7MCyaDRKKBTC7XaTlJSkdZlCxCXdB5AQYvOKq1kwIcTmIgEkhNCMBJAQQjMSQEIIzeg6gKS/LsTmprt1QOFwmIWFBUZGRgAoLi7G5XJpXJUQ4k10F0Dz8/N0d3dz5swZzGYz//Zv/8aePXu0LksI8Qa6CyCfz8fY2Bjff/898/PzuFwuHA4HpaWlsbOhhRCbg+4CyGQy4Xa7yc7O5tmzZ1y7do2UlBTMZvNr1zILIbSnuyb0yl3vqampFBQUkJeXx+TkJGfOnOHOnTtalyeEeIXuRkAre7z8fj+FhYV8+umnzM/P09HRQSAQwOFwUFhYGLsjXgihHd2NgODlBtSVmy+Ki4vZv38/NTU1sXvlBwcHtS5RCIEOR0ArotEowWAQRVEoLS3FarWytLTE4OAgra2tGAwGSktLMZlMWpcqRNzSbQDByxBaWYyYnZ3Nxx9/jN1u59atW3g8Hj7//HPKyso0rlKI+KW7AHo1dBRFid0fr6oq5eXlKIrC8vIyjx494ty5c3i9Xqqrq7UsWYi4pbsAUlU1dtFgJBL50XaM4uJifvvb33LmzBlu3bpFMBiMNaZlnZAQG0t3TWiz2YzVaiUcDuP1egmFQq/9f6PRSGFhIc3NzVRXVzM0NMRf/vIX+vv7NapYiPiluxGQ1WrFZrMRDofx+/0/CqAV27dvJyEhIRY+NpsNi8VCUVGRNKaF2CC6CyCDwYDRaCQSiRAMBmM9oDfJz8/nww8/xGq1cvfuXTweD7/+9a8pLy/fwIqFiF+6CyAgdsXOzx3HoSgKlZWVmEym1xrTHo+HqqoqLBbLRpQrRNzSZQC9q8LCQj7//HPOnTtHd3c38/PzqKpKVVWVPI4JsY4kgHjZmC4uLubw4cMEAgEGBwc5deoUPp+Puro6mR0TYp1IAL1i+/btJCcnc/LkSW7dusXVq1cxm81UVFTIBYZCrAPdTcP/EoqikJ2dzfHjxzlw4AAjIyN8/fXX9Pf3v7WZLYR4P7ocAb26Evp9bNu2DZfLxfLyMr29vVy5coVwOEx1dTVWq3UtSxUirukygFY7C/Y2GRkZfPbZZyQkJHDjxg28Xi82m42KigppTAuxRnQZQBaLhUgkgs/nIxwOv9drKIpCTk4Ohw8fxuv1cu/ePU6fPs3S0hJ79+6V84SEWAO6/C2y2+2EQiGWl5d/ciX0auXn5/Pb3/4Wo9FIZ2cniqLgcDjYtm2bPI4J8QvpsgltNpuJRCL4/f5f3DxWVZW0tDSam5tpampifHyckydP0tvbK/eOCfEL6XIE9GoPaK1CorS0FJfLhc/n486dO7S1taEoCjt27JCRkBDvSZcBtF7S09Njh5p1dnbi8Xgwm81s375dFisK8R4kgN5RQUEBLS0tscb02bNn8Xg81NbWyuyYEO9IAug95OXl8dvf/haTycR3331HNBrF4XBQVlYmj2NCvANdNqHXm6qqpKenc/jwYRoaGpiYmODPf/4zXV1deL1ercsTYsvQ7QhopQH9vquhV6OsrAy3200wGOTmzZtcvXoVVVWprq4mMTFx3b6vEHqh2wDaKGlpaZw4cQKbzUZXVxdnz54lEomwZ88enE6n1uUJsanpMoAURcFisWAymQgGg+v+/YqLi7FarYRCIe7evUtbWxuBQID6+noZCQnxFrrsARkMBhwOBxaLBb/fvyHfMzMzk88++4ympiaePXvG9evXuXv3LvPz8xvy/YXYinQ/AgoEAoTD4XVfp6OqKqmpqTQ1NRGJRLh58yYXLlzA7/dTX1+Py+Va1+8vxFakywCClyGkKArRaJRIJLJhCwVzc3P5+OOPCYfDdHd309nZidFoZPfu3bjd7g2pQYitQrcBpCWXy8XBgwexWCx0dHRw6dIlAGpra6UxLcQrJIDWSUFBAU6nE4/Hw+3bt2lvbycYDEpjWohX6LIJvVkkJyfz4Ycf0tjYyMzMDNeuXePu3bssLCxoXZoQm4KMgNZZRkYGjY2N+P1+bt26xeXLl6UxLcTf6TaAXj2GYz1XQ69GdnY2n376Kaqq0tnZSUdHB2azmerqamlMi7im2wAC1n0rxmopikJiYiJNTU2oqkp3dzcXL14kHA6zd+9eEhIStC5RCE3oMoAURcFkMmE0GgmFQgSDwU1xhnNBQQEulyv2OHbjxg2i0Si1tbXSmBZxSZdNaFVVsdvtmM1m/H4/Ho9H65JikpKSOH78OE1NTczMzNDa2srdu3dZXFzUujQhNpxuA8hqtcZWQvt8Pq1Lek12djZNTU3U1dWxtLTE+fPnaW1tZWpqSuvShNhQ2j+XrBODwYCqqrGV0JulH7QiKyuLf/mXf0FVVdra2mhrawNg3759pKenb6pahVgvug2gzf4L/Gpj2mAw0NPTw40bN4hEIjQ0NJCZmal1iUKsO90G0Fa5MqewsJDMzEwsFgtdXV309PQA0NDQQHp6Oqqqy6dkIQCd9oC2GqvVSmNjI83NzYRCITo6Ouju7ubp06dalybEupIA2iQyMjLYv38/9fX1GAwGurq66OjoYHp6WuvShFg3EkCbSGJiIseOHePAgQMEg0F6enro7u6W2TGhW7oNoFcPpd/sDelXJSYmUldXx8GDB1EUhevXr9PZ2SkhJHRJtwFkMBgwGAyEw2HC4bDW5byTjIwMjh8/Tn19PZFIhO+//z7WE/qld90LsZnoMoBWVkKvnAnt8Xi23C+u1WqloaGBlpYWQqEQN27coKurSxrTQld0G0A2my22FcPr9W6ZaflXZWZmcvDgQfbu3YuiKHR1ddHZ2cnTp0+35PsR4p/pMoAURYmthI5EIoTD4S37C+t0OmlpaeHQoUMEAgG6u7vp7u6W2TGhC7oMIL1JTk5m7969NDU1oSgKN27coLOzU0JIbHkSQFtEWloaH3zwAfX19YRCoVhjenJycsv1t4RYIQG0hdhsNvbt20dzczPhcDi2iXVsbEzr0oR4LxJAW0xWVhbNzc3U1dWhKAq3bt2ivb2d4eHhDbmGWoi1JAG0BTkcDg4dOsTx48exWq10d3dz+fJlRkZGtC5NiHei693wW3El9GqlpaWxf//+2Grp/v7+2PlHJSUlsotebAm6DaBXr2beqlPwP2flBlaz2UxnZyf9/f1Eo1EMBgMFBQUbdh21EO9LlwGkKAoWiwWTyUQwGCQQCOh2pshms7F7926MRiPXrl2jv78fgMbGRioqKjSuToi3020A2Wy22JnQW3Ul9Gq53W727t1LKBSis7OTgYEB4OV2juzsbMxms8YVCvFmugwgVVVfGwH5/X7djoBWWCwWdu/ejclk4urVq7GR0IEDB9i2bZvG1QnxZroMIPjHofRbcTf8+3K73dTU1MQ2r66E0EpPaDPcjSbEq3T7E7nSfFZVVZezYD/FbrfHNq+uzI4pisLhw4cpKiqKq78LsfnpNoDimd1up7q6GkVRaG9vp6+vj2g0SjAYpLy8XOvyhIiRANIpt9sdO9Dsxo0bDAwMxGYHc3JyMJlMWpcohASQnlksFqqrq1FVNTZFrygKTU1NlJWVaV2eEPoNIL2vhF6tpKQk6urqCIfDdHR0xB7HTCYTeXl5slhRaEq3ARQPK6FXy2azUVdXh6qqrzWmDx48SElJidbliTimywBSFAWTyYTRaCQQCBAMBuM+hBISEti1a1dsduzOnTvMzc1x4MAB9uzZI3vHhCZ0GUCqqmK1WjGbzSwtLeHz+eI+gODllT/79u0jGo3S1tZGX18foVAIh8NBUVERVqtV6xJFnNHlx95KAK2shJYA+gez2czOnTs5evQoFRUVTE5OcvbsWXp7e7UuTcQhXY6AAIxGY+xQ+lAoJAH0iqSkJBoaGnC73bS1tTE4OIiiKLGRkM1m07pEESd0G0Di7QwGA6WlpYTDYRRF4cGDB5w5c4YPPviAXbt2aV2eiBO6DaBXRzzxPA3/NhaLhcrKSgwGA6FQiEePHtHa2kooFGLXrl2yd0ysO/kJi3Mmk4ny8nLC4TBms5mBgQECgQB2u52SkhI5ykOsKwkggdFojB3ZEQgEGB4e5ty5cxw4cID6+nqNqxN6ptsAkkewd2O1WqmqqoptYB0YGCAajeJ0OikoKMBut2tdotAh3QaQeHdGo5GysrLY6vGHDx9y5swZjh49Sk1NjdblCR3SZQCtrIReOZBMpuFXz2q1UllZiaIohMNhHj58yNWrVzEYDFRUVEhPSKwpXQbQqyuhZSHiuzOZTFRUVMQ2rQ4ODnL+/PlYCMkGVrFWdBlAiqLEVkL7/X4JoPewMjumKEqsMX3hwgU8Hg979+7VujyhE1sigEKhED6fj1AohKqqmM1mDAYDRqPxjQ3mVzejhsNh2Yz6niwWC1VVVQC0t7czODhIKBTCZrNRVFSEw+HQuEKx1W36AIpEIszPzzM0NMTk5CSKopCRkUFeXh4pKSk/ebKfHMexNgwGA2VlZUQiEaLRKIODg/z5z3/myJEjHDx4UOvyxBa36QMoGo3i9XqZmpqiu7ubkZERtm3bxieffEJKSspb/5wcSLY2VqboDQYDwWCQgYEBrl27FhshJSQkaF2i2KI2fQDBy+lhp9OJx+Oho6ODZ8+e0dLSIlsFNpDJZKKsrAxVVUlMTORvf/sb3377LdFolPr6egl58V42/W+woiixxXBZWVlEIhG8Xi8Wi0V+6DeYxWKhoqICi8USGwldunQJv9/P/v375aB78c42fQCpqordbsfpdJKenk5paSn5+fm43W6tS4tLqqpSXFyM0WgkISGBzs5Orly5gsPhoLKyUlZMi3eyZQ4ke/r0KXNzc2RlZVFWVvazfQfpAa0fRVHIy8tj37591NbWsri4yLfffktPT4/WpYktZtOPgACCwSAPHz7k8ePHJCUlUVpa+tZDsxRFiR1ItrISWqytlZHQymPXzZs3uX79Og6Hg4qKCmlMi1XZEiOgcDjMyMgIT548wel0kp+fj8Vi+cmvX7mAb+VIVr/fTyQS2cCK44OiKOTk5HDw4EEaGhp49uwZp0+f5t69e1qXJraILTMCGh4eZmRkhLq6OvLy8n52T5LNZsNsNuP3+/F6vbIWaJ0YDIZYT8jn83Hv3j2uXLlCOBymrq7urR8UQmyJAFpcXGR6eprFxUVcLhepqak/e42M2WzGZDIRCoUIBAISQOtopSd05MgRbDYb3333HRcvXsRut1NVVSUhJH7Spg+gYDDI9PQ0Ho+HhIQEUlNTV7X+R1ZCbyxVVSksLATA5/PR39/Pt99+y/z8PM3NzRpXJzarTR9AS0tLjI+PYzAYyM/PJzU1dVV/TmbBNp6qqhQVFcX26fX09HD9+nUSExMpLS3F6XRqXaLYZDZ9E3p2dpbx8XFMJhMFBQUkJiZqXZJ4C0VRyM3Npampifr6el68eME333zD3bt3tS5NbEKbfgT07NkzhoaGYkN8WYC4+RkMBkpKSmJXY9+9ezd2qNnOnTtlF72I2fQjoKmpKR49egRAQUGBBNAWsdKYbmlpob6+nunpac6ePcudO3cIBAJalyc2iU09AgqHw4yPj/Po0SN27NhBXl4eLpdr1X9eekDaWpmiXznU7NatW3zzzTfMz89z9OhROd5VbO4AWlxcZHR0lOnpaWpra8nJyVn1D62iKLGrmWURonYURaGoqCh2eFxHRwdXr17F5XKxY8cO6enFuU37CBYKhZiammJycpJAIEBSUlLs/J/VHDK/MhOzshJapuK1s9KYbmlp4cMPPyQUCnHy5Ek6Ozu1Lk1obNOOgLxeL6Ojo/j9fvLz80lLS2NpaYlwOEwkEiE5Ofmtxz+sHN0aCATwer0yCtLYyiRCUlIS4XCYa9eu0d7ejsViYc+ePTISilObNoCWlpYYGhoCoLKyksTEREZHR4lGo9jtdhITE3/2/JmVEZCshN48EhMTOXz4MDabjUuXLnH69GlUVeXgwYM/u7pd6M+m/RdfWFjg/v37zMzM4HK5UBSF+fl5rFYrLpdrVVfDSA9oc8rIyKCxsZGGhgai0Sjnz5/nwoUL+Hw+rUsTG2zTjoDgH7db2Gw27HY7breb3NxcHA7Hqj4tZRZs80pJSeHEiRPY7XbOnz/P5cuXcTqdVFdXy4rpOLJpAygxMZG6ujrcbjdpaWkUFhaSn59PQkKCBIpOJCcns2/fPoLBIN999x1ff/018/Pz/OpXv5J/4zixaQMoKSmJxsZGSktLUVWVnJwckpKStC5LrLHMzEyOHTsGwJUrV2KHmu3evVsa03Fg0waQ2WwmJyeH9PR0otGoLFrTMbfbzYEDBzCZTLS2tnLq1Cmi0ajsoo8DmzaAVo5V/aVX76zMfsmQfnPLzMzkwIEDeDwevvvuOy5dukQwGKSpqUkOutexTTsLtlZWmtUyE7b5paSk8MEHH3D06FFmZ2e5cOECt2/fxuPxaF2aWCe6DiCDwYDZbEZVVYLBoNbliFVISUmhvr6egwcPEg6HOXXqFNeuXZN1XDq1aR/B1oLRaMRut6OqKl6vV+tyxCplZmby4YcfYjQauXz5MlevXsVms7F9+/ZVH0gntgbdj4CsViuqqsoity3G7XbT1NTE8ePH8Xg8fPXVV9y4cUP+HXVG1wGkKAoGgwFFUQiHw1qXI95RVlYWzc3NsRXT165d48KFCzx//lzr0sQa0XUAgcyCbXXJycmcOHGCTz/9lFAoxOXLl7l58yZLS0talybWgK57QEIfXl0x3dHRwcWLF/F4PBw7dky2bWxxuh8BCX1YGQm1tLQQCoW4fv06HR0dzM7Oal2a+AUkgMSWYbFY2Lt3Lx999BEmk4mzZ8/S3t4ujektTPePYNID0pfk5GQOHz5MIBDgypUr3LhxA0VR2L9/v0zRb0G6HwGtBI8sZNMPi8XCoUOH+OSTTwiFQly4cIGbN2/KiuktSNcBZDAYMJlMKIpCMBiUqXgdcblc7N27l0OHDmGz2bh8+TLnz59nfn5e69LEO9B1AL26Etrn88l9VDrjdDr54IMPOH78OIFAgPb2drq6upibm9O6NLFKug6gf14JLQGkPzabjdraWk6cOIHZbObs2bO0tbXJ1pstQtcBtHKkq6IohEIheQTTqeTkZI4cOcKBAwcA6OjooK2tjWfPnmlcmfg5ug6gfyYzYfpltVo5cOAAn3zyCdFolHPnztHd3S0joU1OpuGFbrjdbhoaGlheXub69eu0tbXh8/loamoiIyND6/LEG8TVCEjoX0JCAsePH+fEiRMEAgEuX75MR0cHU1NTWpcm3kACSOiO3W6ntraWY8eO4XA4uHTpEpcvX5Zd9JtQXD2CyWNY/EhKSuLYsWOoqsqlS5e4efMmVquVhoYGcnJytC5P/J3uR0CvroSW1dDxxWq1sn//fr744gscDgcXL17k+vXrsoF1E9H1CEhV1dj98DINH5+SkpLYv38/i4uLtLa20tXVRSQSobm5maysLK3Li3u6HgEZjUZsNhsGg0EWIsYxRVE4fPgwn332GSaTifb2dr777juePn2qdWlxT9cBZDAYsNlsshJaYLVa2bVrFx9++CEpKSm0trZy4cIFWayoMV0HkKqqr62EDoVCWpckNGSz2WhpaeHYsWOYzWZ6enpob29ncnJS69Lilq57QCBNaPFjNTU1GI1Gzp07x4ULF/D7/Zw4cYKkpCStS4s7ug8gmYYX/8zlctHU1MTS0hJXrlyhu7sbRVE4dOiQNKY3mK4fwYR4mwMHDvCb3/wGk8lEW1sbnZ2d0hPaYLofAQnxUxwOBzU1NSwuLnL16lWuXr2Kx+PhxIkTpKWlaV1eXND9CEj6PuJtLBYLR48ejV0F3d3dLXvHNlDcjICkByR+iqqqVFdXE4lEuHjxIhcuXMDj8fCrX/0Kt9utdXm6pusAUhQFo9EoB5KJn+VyuTh06BB+v58LFy7Q3d1NNBpl3759FBYWYjAYtC5Rl3T9CGY0GmNHsvr9flmIKH7Wvn37+M1vfoPRaOT8+fNcuXKFJ0+eyKP8OtH1CGhlK4aqqni9Xgkg8bNWbtuYn5/n2rVr3L59G4AjR45QVFSEqur6M3vD6TqAVFXFbDajKAqBQIBgMKh1SWILMJlMHDt2jIyMDE6fPk1vby8Wi4VoNEpRUZE8jq0hXQcQyEpo8X5MJhPbt28nEolw+fJlenp68Pl8HD9+nIKCAhkJrRHdB5CshBbvy2KxUFdXF7t9dWBgALPZTGNjI8XFxRiNuv/1WXfyNyjEz9ixYwdWq5UzZ85w8+ZNotEoZrOZ/Px8GQn9QhJAQvyMhIQEdu/ezeLiIteuXaO3t5dQKERLSwvFxcUSQr+ABJAQq1RfX09CQgKnTp3i7t27WK1WFEWR2bFfQPcBJD0gsVYsFgtVVVX4/X7a2tro6enB6/Vy/PhxCgsL5efrPeg6gBRFwWAwoCgK4XCYSCSidUlii7NYLDQ0NKAoCufOnWNgYACLxUIoFKKoqEga0+9I139bqqpisVhQVVXWAYk1tX379thq6e7ubiKRCCaTSRrT70jXAWQymbDb7XImtFhzCQkJ1NbW4vF4aGtr4969e0QiEQ4dOkRJSYmE0CrpOoAMBsNrIyB5BBNrra6uDqfTyTfffMPt27cxm80YDAYKCwslhFZB1wEELx/DVhrRVqtV42qE3thsNnbs2MHi4iLXr1/n+++/Z2FhgSNHjlBaWorJZNK6xE1N9wEELzelejwe+vv7cTgca/raiqJgNptxuVykpqZis9nW9PXF5mc0Gjl48CA2m43Tp0/T19eHwWAgGAxSXl6OxWLRusRNS/cBpCgKVquVJ0+e8NVXX/GHP/xhzV/fZrNRXV3N73//e3bs2LGmry+2jsrKSgAuXbrE3bt38fl8AFRUVGA2m7UsbdPSfQC9aj3WAgWDQW7dusXIyAjNzc0SQHHM4XBQV1dHOBymra2N4eFh2traCIfDVFRUyOj4DXQfQJFIBJ/PR2JiIkeOHGHv3r1r+voLCwv853/+J0NDQywvL6/pa4utqbq6GrfbzdmzZ3nw4AGqqqKqKlVVVdIT+ie6D6BoNEowGMRqtVJZWcnu3bvX/HsUFhYyNjYms2wCeNmYLi8vZ2lpCVVVefToUexW3vLycpkMeYXuA2jl0ycQCKzLCGVxcZFAIICiKDLtKl5TU1ODw+HgzJkzDA0NYTKZiEQibN++XXpCf6frADIYDJjN5tiZ0H6/f82/RygUkpGPeCNVVSkpKeGDDz6gtbWV+/fvEwwGMRgM0pj+O10HkNFoxG63Y08ozzMAABFZSURBVDAY8Hq96xJAQryNyWRi586dRCIRQqEQo6Oj0ph+ha4DyGAwyK0YYlPYtm0bNptNGtP/RNcBtLIbHpDd8EJTNpuNbdu2sbCwACCN6b/TdQCBnAckNpddu3bhdDo5ffp0rDEN/9hdH2/i7x0LoSGTyURpaSlHjx6lvb2dH374gWAwiKqqlJeXx11jWgJIiA1mMBioqanBaDQSCAQYGRnh2rVrRCKRuHsckwASQiNlZWWYTCb++te/Mjg4SCQSQVEUqqqq4uZxTPfvUnpAYrOyWq1UVFSwtLRENBpleHgYv9/PwsIC27dvJykpSesS153uA0huRhWb3c6dO3G5XHz77bcMDAywvLxMKBRi//79G36URyQSIRKJxM5Sh3/87qzHh7iuA2hlJfTK3fAr055CbCYWi4WysjIOHz6MyWTi8ePH3LhxA4Ddu3fjdrs3pI7l5WVGR0fxeDxkZ2eTlZXFixcvmJqawmazkZqaisPhWNMtR7oOIFVVsdlsGAwGORNabGqKolBbW0tycjLXrl3j3r17sRCqra3F6XSu2/deWlpienqawcFBRkZGiEajVFdXEwgEuHPnDvfv36eyspJ9+/Zht9vX9HvrPoDWeyX0q0NS6TGJX6qgoICWlhYUReHevXtcv36dSCTCvn371vw0T3g56uno6ODKlSuMjIyQkJBATk4OExMTjI+Pc/r0aZ48eYLD4aCxsXHNN1zrOoDg5X4wRVGIRqPr8jztdrtjB5Gvxw+IiC+qqpKfn8/HH39MUlISvb299PX14XQ6qaysJCEhYc2+19LSEtevX+frr7/m3r17ZGVlUV5eTn5+Pi6Xi97eXrq6upifnycUCmG32+OrB7TSEFvx6taK1YpGo0QiEQKBAPPz82u+IXV2dpbl5WX8fj8vXryQDa/iF1n5GbdYLFRUVDA5OUlfXx/Pnz9nbm6OxsZGbDbbmoxEent7+cMf/sDt27fZuXMnn3/+OU1NTVitVp49e8b9+/dRFAWn00lqauq6fIBv2gB68uQJw8PDTE1Nsby8TDAYxO12U1xcTFlZGS6Xa9WvFQ6HGR4e5quvvmJ0dHRN6/T5fLS3tzMxMcF///d/09XVtaavL+LTytlBg4OD3L9/n3A4zL1795iZmaGpqYmCgoIf/ZlgMMjc3FxsxPLqrO9KOyI9PR2LxcLExASXLl3i4sWLJCcnc+LECVpaWkhJSQHA4/GgqipZWVkkJiaSmZm5Li2GTRVAPp+P58+f8/jxYx4+fMj4+DjPnz9nYWEBn8+HxWIhIyODXbt2sXv3bgoLC3921ajZbCY3N5e8vDyeP3/OuXPn1rxus9lMQUEBw8PDax5wIj6tTHmHw+HYFPjU1BT379//yXPHvV4vfX199Pb2Mjs7Szgcjv0/s9lMTk4Ohw4dIiUlhe7ublpbWwkGgzQ0NNDc3BwLH4CpqSlGR0dxu93s3r2b9PT0dXmfmyaAQqEQPT09nD9/PnbBW2VlJdu2bYsdq/rgwQMuX77MxYsXaWpq4ne/+x379+9/63DUbrfT0tJCZmYmc3NzsZsK1oqiKDgcjtjVPzLTJtaKoiiYTKbYqmir1Up2djaZmZlv/Hqv10tvby+nTp1iaGjotWUnDoeDmpoa8vPzCQaD3Lhxgx9++IGdO3dy7NgxcnJyXnutkZERurq6MJvNlJSUvBZOa2lTBND4+DidnZ1cvHiR/v5+otEou3fvZs+ePVRXV2O1WolGo9y6dYvZ2VkuXbrEyZMncTgcZGZmkp+f/5NnqpjNZsrLyykvL9/gdyXExopGo4TDYQKBAH6//7UAMpvNhEIhFhYWCIfD9PX1EQwGaWpqoqGh4bXeqsfj4cGDBzx48IDt27eTm5tLYmLiutSseQCNjY3x9ddf88c//pGZmRn279/PBx98QG1tLampqbhcrthfjtPpJDMzk4SEBL7++msuX75MRUVFLIiEiGc2m43Kykq8Xi/Pnz9/7RHM4XCQk5NDQkICY2NjzMzM4HK5KC0tJScnJ9bfCYVCDA8P8/DhQ4LBIOnp6eTk5KzbyY2aBtDs7Cx//etf+fLLLxkcHKS+vp7PPvuMY8eOvXG6MSkpiX379jE2NsbNmzd59OgRN27cYMeOHRJAIu7ZbDZ27txJbm4uwWDwtRlks9mMxWJheXmZu3fvsri4SGJiIvn5+a/Nbs3MzDAwMMCDBw8IBAKkpqauWwMaNAyglZ7PH//4R+7cucP+/fv5j//4D44cOfKzax0yMjIoKCjg/v379Pf3Mz09vUFVx6eVJqjY3MxmM1lZWbEP41dnwVb+/SYmJjCbzYTDYbxeL3NzcywuLqIoCj6fj7GxMSYnJ/F6vTgcjthTyHrRLID6+/s5efIkHR0d2O12Pv74Y44ePbqqN2u1WrHb7fj9fsbHx5mfn9+AiuPPSvPf4/HEDs2yWq2YTCZMJpOE0ib0cxtGU1JSKCgowOl08vDhQ86cOcPCwgLJycmkpKTErq7Kzc3F5XKRn5+/rtdNbXgARaNRPB4P169fp7W1lUgkQmNjI4cPHyYtLW1Vr7G8vMzz588JhUIYjca4OTtlo0UiEWZnZ/nhhx94/PgxgUCAgoICtm/fTlZWlgTQFmSz2aioqODgwYP4/X6GhoZwOp1UVVWRmJiI2WwmEomQkpJCcXEx+fn561rPhv/mBgIB7t+/T3d3N5OTk5SUlHDkyBHy8vJW/RozMzOx9TY5OTnr1qGPd5FIhLm5Ofr6+mKX6x04cIDk5GSys7O1Lk+8p5ycHH73u99RUFDAs2fPyM3NZffu3RQVFTE+Ph57qqiqqlr33uqGB9DCwgK9vb3cu3cPeHncQGNj46qfM5eWlhgbG+PFixc4HA62bdtGamrqepYct1RVxW63U1BQgM1mo6+vD5fLFTu5T2xNdrudffv2kZ+fz9TUFA6Hg5KSEmw2G1NTUzx8+JDZ2VkyMjL0F0ArQ/qxsTHMZjOlpaUUFRWtap9JKBRiZGSEBw8e4Pf7ycnJobKyct0WScU7VVXJzMzE5XIxMjLC3/72t1ivQGxtZrOZ/Px8srKyUFU11saYmZnhyZMnmM1mMjMz1/1Uxg2/zHx+fp5Hjx7x4sULjEYj2dnZJCcnr+rPBgIBBgYGuHPnDouLixQXF1NbWyu/EOtkZSVuMBiMLeisrKxc17NpxMZRFAWz2RwLn3A4zPj4OC9evMBut5Odnb3uI90ND6ClpSVGR0cJBoPAywVSq93hPjMzQ09PDz/88AOJiYnU1NTEFiKK9eH3++nt7eXx48fk5eWxY8eOuLq1Qe+i0Sg+n4/p6WmuXr3KtWvXeP78eWwf2quLGdfDhj+C+Xw+nj17Brx886sNn0AgQF9fH11dXfh8Pg4ePEhjY6OMftZZIBCInUqQmZlJYWFh3N1dpWder5fR0VFu3rzJ2bNnaW1tZW5ujuXlZYaGhtZ9kmfDR0Amkyk2hF/t8C4ajdLV1cWXX37JnTt3KCgo4JNPPqGmpmZd1yiIl8Pyx48fMzIygtPpJDc3N67vMteTUCjE7Owsw8PD9Pf3Mzo6isViYdu2baSlpTE9Pb3ua+w2fASUkpLCjh076OvrIxqNMjc399avj0Qi9PX18eWXX3LmzBmMRiNHjhzh4MGDP9mhf/UgM1VVJaR+AZ/Px9DQEGNjYzidTjIyMt75UDixOYVCIbxeL6FQiMzMTI4ePUokEsFoNOJyuUhKStLfI1hGRgZ1dXVcv36dqakp/va3v/HgwQPKysp+9LWBQIC2tja+/PJLvv76awwGA5999hn/+q//Smlp6Rt/ERYWFujv7+fx48dEo1Hy8/OpqKhY9SJH8bqZmRkmJibw+XwkJSWt6ZGgQlsGg4HExERKSkrIzs5GVdXY43U0GsVsNq/7GrsNDyC3201NTQ1NTU389a9/pbOzk//3//4fH330ERkZGcDLk91WPnlPnTpFe3s7iYmJfPLJJ/z7v/87+/bt+9Hjm9/vZ2Jigvv37zMwMMDQ0BDLy8tkZGSwuLgYW2sko6HVW9kbFAqFSEtLk36bzphMJlJTU0lJSXnjFo6NuEdvwwPIZrOxY8cOPv74Y2ZnZ+nu7uZ//ud/6O3tpbS0FJPJxNzcHNPT08zNzRGJRDh8+DC1tbU0NTVRUVHxxt7R4OAgf/rTn5icnKS4uJjt27czPj7ODz/8QCgUIjExkR07dsiq6XewcieU0+kkLy8vLm7qjDdv2zu2EYtNNzyAFEXB7XZz+PBhVFUlJSWF9vZ2Ll26xMjICBUVFUQiERYWFrBarezevZsTJ05QW1v7xubnSiPt1q1b3L59G7fbzc6dO9m5cycjIyN4PB6eP3/ODz/8QHZ2tgTQO3j69CmTk5MkJSVRUVEhf3dizWm2izMzM5Njx46Rnp5OamoqXV1dFBQUcPz48djxkC6Xi5SUFDIyMn5y5mVpaYmOjg4GBwepqKigvr6epqYm3G43BoOBiooKHj58iM/ni+30FaszNTXF8PAwFouFoqKidT2WQcQnTbeRR6NRQqEQRUVFFBcXU15eTk1Nzc+ujF5aWoodITA3N8fVq1cZGhriiy++4MiRI7FehclkYnZ2loWFBSwWy7qd6qZXT548YXBwkNLS0thdUUKspQ0PoEgkgs/ni51mePPmTZKSkvjkk0/YtWvXW2dZotEoS0tLTE5O4vF4cDqdLC0t0d/fz+zsLAUFBbGNqeFwmIGBAa5fv47BYCAzM1OaqO/A6/UyPDzM0NAQlZWV5Obmrvm1vEJseAAtLy9z+/ZtTp48SWtrK4FAgJqaGu7du0c4HCYnJ4fCwsI3bk5dWlri/v37LC4ukpWVFTu7ZOUepFdHToODg7S2tjI6OsqePXsoKSmRPUyrFI1Gefr0KRMTE3i9Xjl+Q6ybDQ2gSCTC8vIyExMTTExMEA6HSUtLIxwO09bWRnt7O5mZmVRWVlJQUEBiYiImkwmDwYDVasXn8/HixQsSEhLIzMyMPVZlZmby5MkTOjo6YgeV3bhxg/7+fqqqqmhpaSEvL08W0K2Sz+djdHSU5eVl0tPTY2tE5ubmUBSFhIQE+bsUALFbOFbWEL3rzNmGBtDKJWtZWVl8+umnHDp0CI/Hw8zMDI8ePaK/v5+rV6/idDpJTk4mPz8/tvgtMzOTkpISiouLycvLi41mXC4XdXV1zM3N8ac//QlFUTAajfj9foqLi/noo49oaGiQx4d3sLi4yJMnT1BVlW3btpGSksLMzAzT09OxI1QkgAQQu4HDYrGQnp6+uQNIURTsdjvbtm2jqqoKRVFipxuWlZVRUlLC8PBw7I71aDSKzWYjNTWV5ORk0tPTyc/Pf+1Ry+VycezYMcxmM3fu3GF2dpaEhAQqKytpbGykublZpo/f0dzcHENDQxgMBsrLyzEajUxMTGAwGN7rU07oVzAYZGFhAbvd/l4LFzc0gAwGA06nE6fTGVuR7Ha7KSwsJBgMEggE8Hq9TE1N8fTpUwwGAxkZGWRlZWGxWGL/vcpqtVJTU0Nubi6NjY0sLy/H7rJOS0uTkc97WHnUhZf/PuFwmFAo9NpjsRDwcq+lxWJ57xMSNnwE9M+fngaDIdbjWZGbm4vP5yMUCuFwON76ibtyqFJOTg7p6emEw2EsFot8Sv8CJpMJh8NBNBpleXkZi8USOx1PLgAQr7JaraSlpWE0Gt9rm9Om/Wl6n0OvVq6LEb9MUlISNTU1WK1WXC4XeXl55ObmSviIH3nTU8m7UKIbseNMbCl+vz+2gFNVVVJTU3G73VqXJXRIAkgIoRk5m0IIoRkJICGEZiSAhBCakQASQmhGAkgIoRkJICGEZiSAhBCakQASQmhGAkgIoRkJICGEZiSAhBCakQASQmhGAkgIoRkJICGEZiSAhBCakQASQmhGAkgIoRkJICGEZiSAhBCakQASQmhGAkgIoZn/D6TZv9co0WXRAAAAAElFTkSuQmCC)
A hollow conducting sphere is placed in an electric field produced by a point charge placed at P as shown in figure.
be the potentials at points A, B and C respectively. Then
![](data:image/png;base64,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)
A hollow conducting sphere is placed in an electric field produced by a point charge placed at P as shown in figure.
be the potentials at points A, B and C respectively. Then
![](data:image/png;base64,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)
The figure shows electric potential V as a function of
. Rank the four regions according to the magnitude of
-component of the electric field E within them, greatest first
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)
The figure shows electric potential V as a function of
. Rank the four regions according to the magnitude of
-component of the electric field E within them, greatest first
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)
The general solution of the equation
is
The general solution of the equation
is
Solution of
is given by
Solution of
is given by
Equation of the curve passing through (3, 9) which satisfies the differential equation
is
Equation of the curve passing through (3, 9) which satisfies the differential equation
is
If
and f(1) = 2, then f(3) =
If
and f(1) = 2, then f(3) =
The degree and order of the differential equation of all tangent lines to the parabola x2 = 4y is:
The degree and order of the differential equation of all tangent lines to the parabola x2 = 4y is:
The differential equation of all non-horizontal lines in a plane is :
The differential equation of all non-horizontal lines in a plane is :
The differential equation of all non-vertical lines in a plane is :
The differential equation of all non-vertical lines in a plane is :
The differential equation of all conics with the coordinate axes, is of order
The differential equation of all conics with the coordinate axes, is of order
If the algebraic sum of distances of points (2, 1) (3, 2) and (-4, 7) from the line y = mx + c is zero, then this line will always pass through a fixed point whose coordinate is
If the algebraic sum of distances of points (2, 1) (3, 2) and (-4, 7) from the line y = mx + c is zero, then this line will always pass through a fixed point whose coordinate is