Physics-
General
Easy

Question

A long insulated copper wire is closely wound as a spiral of N turns. The spiral has inner radius a and outer radius b. The spiral lies in the X minus Y plane and a steady current I flows through the wire. The Z-component of the magnetic field at the centre of the spiral is

900553

  1. fraction numerator mu subscript 0 end subscript N I over denominator 2 left parenthesis b minus a right parenthesis end fraction ln invisible function application open parentheses fraction numerator b over denominator a end fraction close parentheses    
  2. fraction numerator mu subscript 0 end subscript N I over denominator 2 left parenthesis b minus a right parenthesis end fraction ln invisible function application open parentheses fraction numerator b plus a over denominator b minus a end fraction close parentheses    
  3. fraction numerator mu subscript 0 end subscript N I over denominator 2 b end fraction ln invisible function application open parentheses fraction numerator b over denominator a end fraction close parentheses    
  4. fraction numerator mu subscript 0 end subscript N I over denominator 2 b end fraction ln invisible function application open parentheses fraction numerator b plus a over denominator b minus a end fraction close parentheses    

The correct answer is: fraction numerator mu subscript 0 end subscript N I over denominator 2 left parenthesis b minus a right parenthesis end fraction ln invisible function application open parentheses fraction numerator b over denominator a end fraction close parentheses


    If we take a small strip of d r at distance r from centre, then number of turns in this strip would be,
    d N equals open parentheses fraction numerator N over denominator b minus a end fraction close parentheses d r
    Magnetic field due to this element at the centre of the coil will be
    d B equals fraction numerator mu subscript 0 end subscript open parentheses d N close parentheses I over denominator 2 r end fraction equals fraction numerator mu subscript 0 end subscript N I over denominator 2 open parentheses b minus a close parentheses end fraction fraction numerator d r over denominator r end fraction
    B equals not stretchy integral subscript r equals a end subscript superscript r equals b end superscript d B equals fraction numerator mu subscript 0 end subscript N I over denominator 2 open parentheses b minus a close parentheses end fraction ln invisible function application open parentheses fraction numerator b over denominator a end fraction close parentheses

    Related Questions to study

    General
    biology

    In angiosperms, female gametophyte is represented by

    In angiosperms, female gametophyte is represented by

    biologyGeneral
    General
    physics

    A particle is projected vertically upwards with velocity .30 ms-1 Find the ratio of average speed and instantaneous velocity after 6s.[g=10 ms-1 ]

    A particle is projected vertically upwards with velocity .30 ms-1 Find the ratio of average speed and instantaneous velocity after 6s.[g=10 ms-1 ]

    physicsGeneral
    General
    Maths-

    y equals f left parenthesis x right parenthesis equals fraction numerator x over denominator 1 plus vertical line x vertical line end fraction comma x element of R comma y element of R text  is  end text

    y equals f left parenthesis x right parenthesis equals fraction numerator x over denominator 1 plus vertical line x vertical line end fraction comma x element of R comma y element of R text  is  end text

    Maths-General
    parallel
    General
    physics

    A particle moves 4 m in the south direction. Then it moves 3 m in the west direction. The time taken by the particle is 2 second. What is the ratio between average speed and average velocity

    A particle moves 4 m in the south direction. Then it moves 3 m in the west direction. The time taken by the particle is 2 second. What is the ratio between average speed and average velocity

    physicsGeneral
    General
    physics-

    In the adjacent figure is shown a closed path P. A long straight conductor carrying a current I passes through O and perpendicular to the plane of the paper. Then which of the following holds good?

    In the adjacent figure is shown a closed path P. A long straight conductor carrying a current I passes through O and perpendicular to the plane of the paper. Then which of the following holds good?

    physics-General
    General
    physics-

    A current I enters a circular coil of radius R, branches into two parts and then recombines as shown in the circuit diagram

    The resultant magnetic field at the centre of the coil is

    A current I enters a circular coil of radius R, branches into two parts and then recombines as shown in the circuit diagram

    The resultant magnetic field at the centre of the coil is

    physics-General
    parallel
    General
    physics-

    The figure shows the cross-section of a long cylindrical conductor of radius a carrying a uniformly distributed current i. The magnetic field due to current at P is

    The figure shows the cross-section of a long cylindrical conductor of radius a carrying a uniformly distributed current i. The magnetic field due to current at P is

    physics-General
    General
    physics

    Rohit completes a semi circular path of radius R in 10 seconds. Calculate average speed and average velocity in ms-1.

    Rohit completes a semi circular path of radius R in 10 seconds. Calculate average speed and average velocity in ms-1.

    physicsGeneral
    General
    physics-

    If Young’s modulus of elasticity Y for a material is one and half times its rigidity coefficient eta comma the Poisson’s ratio sigma will be

    If Young’s modulus of elasticity Y for a material is one and half times its rigidity coefficient eta comma the Poisson’s ratio sigma will be

    physics-General
    parallel
    General
    physics-

    Four wires of the same material are stretched by the same load. Which one of them will elongate most if their dimensions are as follows

    Four wires of the same material are stretched by the same load. Which one of them will elongate most if their dimensions are as follows

    physics-General
    General
    physics-

    A current i is flowing through the loop. The direction of the current and the shape of the loop are as shown in the figure.
    The magnetic field at the centre of the loop is fraction numerator mu subscript 0 end subscript i over denominator R end fraction times.
    left parenthesis M A equals R comma blank M B equals 2 R comma blank angle D M A equals 90 degree

    A current i is flowing through the loop. The direction of the current and the shape of the loop are as shown in the figure.
    The magnetic field at the centre of the loop is fraction numerator mu subscript 0 end subscript i over denominator R end fraction times.
    left parenthesis M A equals R comma blank M B equals 2 R comma blank angle D M A equals 90 degree

    physics-General
    General
    physics-

    A part of a long wire carrying a current i is bent into a circle of radius r as shown in figure. The net magnetic field at the centre O of the circular loop is

    A part of a long wire carrying a current i is bent into a circle of radius r as shown in figure. The net magnetic field at the centre O of the circular loop is

    physics-General
    parallel
    General
    physics-

    A wire shown in figure carries a current of 40 A. If r equals 3.14 blank c m, the magnetic field at point P will be

    A wire shown in figure carries a current of 40 A. If r equals 3.14 blank c m, the magnetic field at point P will be

    physics-General
    General
    physics

    A car covers one third part of its straight path with speed V1 and the rest with speed V2 . What is its average speed ?

    A car covers one third part of its straight path with speed V1 and the rest with speed V2 . What is its average speed ?

    physicsGeneral
    General
    physics

    A bus travels between two points A and B. V1 and V2 are it average speed and average velocity then

    A bus travels between two points A and B. V1 and V2 are it average speed and average velocity then

    physicsGeneral
    parallel

    card img

    With Turito Academy.

    card img

    With Turito Foundation.

    card img

    Get an Expert Advice From Turito.

    Turito Academy

    card img

    With Turito Academy.

    Test Prep

    card img

    With Turito Foundation.