Electrostatic Potential and Capacitance Test

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Electrostatic Potential and Capacitance Test - 2

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Question 1
4 / -1

Which of the following statement is not true?

A
Electrostatic force is a conservative force.

B
Potential at a point is the work done per unit charge in bringing a charge from any point to infinity.

C
Electrostatic force is non-conservative.

D
Potential is the product of charge and work.

Solution

Work done by the electrostatic force is independent of the path followed by it, and it depends only on the initial and final positions. For example, work done in moving a unit positive charge in a closed loop of an electric field is zero.
Question 2
4 / -1

1 volt is equivalent to

A

B

C

D

Solution

Volt is the electrical unit of potential difference or voltage, and is expressed as V. One Volt is described as one joule of energy consumption per one coulomb electric charge.
Question 3
4 / -1

The work done in bringing a unit positive charge from infinite distance to a point at distance x from a positive charge Q is W. Then the potential ϕ at that point is

A
WQ/x

B
W

C
W/x

D
WQ

Solution

Electric potential at a point in an electric field is defined as the work done in bringing a unit positive charge from infinity to that point.
Or, V = W/q
Since charge is of magnitude unity, Hence electric potential at that point will be equal to the workdone ∴ ϕ = W
Question 4
4 / -1

The potential at a point due to a charge of 5×10⁻⁷C located 10cm10cm away is

A
3.5 × 10⁵V

B
3.5 × 10⁴V

C
4.5 × 10⁴V

D
4.5 × 10⁵V

Solution

Here, q = 5 × 10(−7) C, r = 10 cm = 0.1 m
Question 5
4 / -1

In the question number 4, work done in bringing a charge of 4 x 10^-9 C from infinity to that point is

A
2.4 × 10⁻⁴J

B
1.8 × 10⁻⁴J

C
3.2 × 10⁻⁵J

D
4.1×10⁻⁵J

Solution

Work done, W = q(V_f − V_i) = 4 × 10⁻⁹ × 4.5 × 10⁴ = 1.8 × 10⁻⁴ J
Question 6
4 / -1

The electric field intensity at a point P due to point charge q kept at point Q is 24 N C⁻¹ and the electric potential at point P due to same charge is 12 J C⁻¹. The order of magnitude of charge q is

A
10⁻⁶ C

B
10⁻⁷ C

C
10⁻¹⁰ C

D
10⁻⁹ C

Solution

Electric field of a point charge.

Electric potential of a point charge,

The distance PQ is r = V/E = 12/24 = 0.5 m
∴ Magnitude of charge
q' = 4πε₀Vr

= 10⁻⁹ C
Question 7
4 / -1

The electric potential at a point in free space due to charge Q coulomb is Q x 10¹¹ volts. The electric field at that point is

A
12πε₀Q x 10²⁰ volt/m^-1

B
4πε₀Q x 10²² volt/m^-1

C
12πε₀Q x 10²² volt/m^-1

D
4πε₀Q x 10²⁰ volt/m^-1

Solution

The electric potential due to charge Q is

where r is the distance of observation point from the charge. At the same point, electric field is

Combining Eqs. (i) and (ii), we have

= 4πε₀Q × 10²² V/m^-1
Question 8
4 / -1

Two points A and B are located in diametrically opposite directions of a point charge of +2μC at distances 2m and 1m respectively from it. The potential difference between A and B is

A
3 × 10³V

B
6 × 10⁴V

C
−9 × 10³V

D
−3 × 10³V

Solution

Here, q = 2 μC = 2 × 10⁻⁶ C,
r_A = 2m, r_B = 1m

= −9 × 10³ V
Question 9
4 / -1

A charge +q is placed at the origin O of x-y axes as shown in the figure. The work done in taking a charge Q from A to B along the straight line AB is

A

B

C

D

Solution

Potential at point A is
Potential at point B is
Work done in taking a charge Q from A to B is,
Question 10
4 / -1

As per this diagram a point charge +q is placed at the origin O. Work done in taking another point charge −Q from the point A [coordinates (0, a)] to another point B [coordinates (a, 0)] along the straight path AB is

A
zero

B

C

D

Solution

Work done is equal to zero because the potential of A and B are the same

No work is done if a particle does not change its potential energy
i. e. initial potential energy = final potential energy.