Maths-

General

Easy

Question

# The solution of is

Hint:

### In the question we have to integrate the given function.

## The correct answer is:

### Related Questions to study

physics-

### For the given figure, calculate zero correction.

### For the given figure, calculate zero correction.

physics-General

physics-

### Three capacitors are connected as shown in the figure to a battery of volt. If the capacitor breaks down electrically the change in total charge on the combination of capacitors is

Since, are parallel to their equivalent capacitance will be . Now, are in series, so the net equivalent capacitances of circuit.

Since, is the voltage of the battery, so charge on this system

If the capacitor breaks down then total equivalent capacitance

New charge stored

Change in total charge

Since, is the voltage of the battery, so charge on this system

If the capacitor breaks down then total equivalent capacitance

New charge stored

Change in total charge

### Three capacitors are connected as shown in the figure to a battery of volt. If the capacitor breaks down electrically the change in total charge on the combination of capacitors is

physics-General

Since, are parallel to their equivalent capacitance will be . Now, are in series, so the net equivalent capacitances of circuit.

Since, is the voltage of the battery, so charge on this system

If the capacitor breaks down then total equivalent capacitance

New charge stored

Change in total charge

Since, is the voltage of the battery, so charge on this system

If the capacitor breaks down then total equivalent capacitance

New charge stored

Change in total charge

physics-

### The charge deposited on capacitor the circuit is

As the capacitors 4 and 2 are connected in parallel and are in series with 6 capacitor, their equivalent capacitance is

Charge in the circuit

Since, the capacitors and 2 are connected in parallel, therefore potential difference across them is same.

Also

or

### The charge deposited on capacitor the circuit is

physics-General

As the capacitors 4 and 2 are connected in parallel and are in series with 6 capacitor, their equivalent capacitance is

Charge in the circuit

Since, the capacitors and 2 are connected in parallel, therefore potential difference across them is same.

Also

or

Maths-

### If then y satisfies

### If then y satisfies

Maths-General

physics-

### In the figure, a proton moves a distance d in a uniform electric field E as shown in the figure. Does the electric field do a positive or negative work on the proton? Does the electric potential energy of the proton increase or decrease?

Since, the proton is moving against the direction of electric field so, work is done by the proton against electric field. It implies that electric field does negative work on the proton.

Again, proton is moving in electric field from low potential region to high potential region hence, its potential energy increases.

Again, proton is moving in electric field from low potential region to high potential region hence, its potential energy increases.

### In the figure, a proton moves a distance d in a uniform electric field E as shown in the figure. Does the electric field do a positive or negative work on the proton? Does the electric potential energy of the proton increase or decrease?

physics-General

Since, the proton is moving against the direction of electric field so, work is done by the proton against electric field. It implies that electric field does negative work on the proton.

Again, proton is moving in electric field from low potential region to high potential region hence, its potential energy increases.

Again, proton is moving in electric field from low potential region to high potential region hence, its potential energy increases.

maths-

### Solution of is

### Solution of is

maths-General

physics-

### Two charges and are placed 30 cm apart, as shown in the figure. A third charge is moved along the arc of a circle of radius 40 cm from C to D. The change in the potential energy of the system is where k is

When charge is at , then its potential energy is

Where charge is at , then

Hence, change in potential energy

Where charge is at , then

Hence, change in potential energy

### Two charges and are placed 30 cm apart, as shown in the figure. A third charge is moved along the arc of a circle of radius 40 cm from C to D. The change in the potential energy of the system is where k is

physics-General

When charge is at , then its potential energy is

Where charge is at , then

Hence, change in potential energy

Where charge is at , then

Hence, change in potential energy

physics-

### Figure shows three spherical and equipotential surfaces A, B and C round a point charge q. The potential difference. If and be the distance between them. Then

Potential difference between two equipotential surfaces A and B.

Or

Or

Similarly,

Since,

therefore

Or

Or

Similarly,

Since,

therefore

### Figure shows three spherical and equipotential surfaces A, B and C round a point charge q. The potential difference. If and be the distance between them. Then

physics-General

Potential difference between two equipotential surfaces A and B.

Or

Or

Similarly,

Since,

therefore

Or

Or

Similarly,

Since,

therefore

physics-

### Charges +q and –q are placed at points A and B respectively which are a distance apart, C is the mid-point between A and B. The work done in moving a charge+ along the semicircle CRD is

In Ist case, when charge is situated at C

Electric potential energy of system

In IInd case, when charge is moved from C to D.

Electric potential energy of system in that case

Electric potential energy of system

In IInd case, when charge is moved from C to D.

Electric potential energy of system in that case

### Charges +q and –q are placed at points A and B respectively which are a distance apart, C is the mid-point between A and B. The work done in moving a charge+ along the semicircle CRD is

physics-General

In Ist case, when charge is situated at C

Electric potential energy of system

In IInd case, when charge is moved from C to D.

Electric potential energy of system in that case

Electric potential energy of system

In IInd case, when charge is moved from C to D.

Electric potential energy of system in that case

physics-

### 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

The electric potential on the surface of shell

Or

Or

### 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

physics-General

The electric potential on the surface of shell

Or

Or

physics-

### Work required to set up the four charge configuration (as shown in the figure) is

Work is required to set up the four charge configuration

### Work required to set up the four charge configuration (as shown in the figure) is

physics-General

Work is required to set up the four charge configuration

physics-

### The points resembling equal potentials are

The points S and R are inside the uniform electric field, so these will be at equal potential.

### The points resembling equal potentials are

physics-General

The points S and R are inside the uniform electric field, so these will be at equal potential.

physics-

### 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

When a positive charge is moved from one point to another in an electric of magnetic field, then under the influence of the field force acts on the particle and an external agent will have to do work against this force. But in the given case the charge moves under influence of no field, hence it does not experience any force therefore, no work is done.