Electrostatics MSQ

*Multiple options can be correct

QUESTION: 1

A wire having a uniform linear charge density is bent in the form of a ring of radius R. Point A as shown in the figure, is in the plane of the ring but not at the centre. Two elements of the ring of lengths a₁ and a₂ subtend very small same angle at the point A. They are at distances r₁ and r₂ from the point a respectively.

A.
The elements a₁ and a₂ produce same potential at A
B.
The ratio of charge of elements a₁ and a₂ is r₁/r₂
C.
The element a₁ produced greater magnitude of electric field at A than element a₂
D.
The direction of net electric field at A is towards element a₂

Solution:

i.e. Net field at A is towards a.

The correct answers are: The ratio of charge of elements a₁ and a₂ is r₁/r₂, The element a₁ produced greater magnitude of electric field at A than element a₂, The elements a₁ and a₂ produce same potential at A, The direction of net electric field at A is towards element a₂

*Multiple options can be correct

QUESTION: 2

In front of an earthed conductor a point charge +q is placed as shown in figure :

A.
On the surface of conductor the net charge is negative.
B.
On the surface of conductor at some points charges are negative and at some points charges may be positive distributed non uniformly
C.
Inside the conductor electric field due to point charge is non zero
D.
None of these

Solution:

Charge is distributed over the surface of conductor in such a way that net field due to this charge and outside charge q is zero inside. Field due to only q is non-zero.

The correct answers are: On the surface of conductor the net charge is negative., On the surface of conductor at some points charges are negative and at some points charges may be positive distributed non uniformly, Inside the conductor electric field due to point charge is non zero

*Multiple options can be correct

QUESTION: 3

Two concentric rings of radii R₁ = and R₂ = 4m are placed in yz plane with their centres at origin. They have uniform charge –q and on the inner and outer rings respectively.

A.
Where potential is maximum on the x-axis, field intensity is zero
B.
The electric field intensity is zero at r = 2m
C.
The electric potential is zero at origin
D.
A positive charged particle disturbed from origin along the x-axis will restore back to origin

Solution:

V at origin ≠ 0

0

From origin to r = 2, field is towards origin.

The correct answers are: The electric field intensity is zero at r = 2m, A positive charged particle disturbed from origin along the x-axis will restore back to origin, Where potential is maximum on the x-axis, field intensity is zero

*Multiple options can be correct

QUESTION: 4

The diagram shows part of an evacuated tube in which a stream of electrons from an electron gun passes between a pair of parallel large deflecting plates. The vertical displacement of the electron beam as it leaves the parallel plates is x. (Do not consider gravity and the electron enter the deflecting region parallel to the plates)

Which one of A to D below will change the displacement x of the beam as it leaves the parallel plates

A.
increasing the distance between the electron gun and the deflecting plates
B.
increasing the accelerating voltage
C.
increasing the deflecting voltage
D.
increasing the distance between the two deflecting plates

Solution:

Increasing the accelerating voltage means increasing speed of the electron, thereby decreasing time spent between the plates. It will reduce x.
Increasing deflecting voltage means increasing electric field between the plates, making acceleration of electron greater. Increasing distance once again will change electric field between the plates.

The correct answers are: increasing the accelerating voltage, increasing the deflecting voltage, increasing the distance between the two deflecting plates

*Multiple options can be correct

QUESTION: 5

In the figure shown, initially the spring of negligible mass is in undeformed state and the block has zero velocity E is a uniform electric field, then : (K = spring constant)

A.
The maximum speed of the block will be
B.
The maximum compression of the spring will be
C.
The maximum compression of the spring will be
D.
The maximum speed of the block will be

Solution:

Speed will be maximum when acceleration becomes zero. i.e. when Kx = EQ

By work-energy theorem :

The correct answers are: The maximum speed of the block will be The maximum compression of the spring will be

*Multiple options can be correct

QUESTION: 6

A particle of mass 2kg and charge 1mC is projected vertically with a velocity 10ms^–1. There is a uniform horizontal electric field of 10⁴N/C.

A.
the time of flight of the particle is 2sec
B.
the horizontal range of the particle is 10m
C.
the horizontal range of the particle is 0m
D.
the maximum height reached is 5m

Solution:

The correct answers are: the horizontal range of the particle is 10m, the time of flight of the particle is 2sec, the maximum height reached is 5m

*Multiple options can be correct

QUESTION: 7

An electric dipole is placed at the centre of a sphere. Mark the correct options.

A.
The electric field is not zero at any where on the sphere
B.
The electric field is zero on a circle on the sphere
C.
The flux of the electric field through the sphere is zero
D.
The electric field is zero at every point of the sphere

Solution:

The correct answers are: The flux of the electric field through the sphere is zero, The electric field is not zero at any where on the sphere

*Multiple options can be correct

QUESTION: 8

The figure shows a charge q placed inside a cavity in an uncharged conductor. Now if external electric field is switched on

A.
both induced charge on outer and inner surface will redistribute.
B.
only induced charge on inner surface will redistribute.
C.
only induced charge on outer surface will redistribute.
D.
force on charge q placed inside the cavity will change.

Solution:

The distribution of charge on the outer surface, depends only on the charges outside, and it distributes itself such that the net, electric field inside the outer surface due to the charge on outer surface and all the outer charges is zero. Similarly the distribution of charge on the inner surface, depends only on the charges inside the inner surface, and it distributes itself such that the net, electric field outside the inner surface due to the charge on inner surface and all the inner charges is zero.
Also the force on charge inside the cavity is due to the charge on the inner surface.

The correct answers are: only induced charge on inner surface will redistribute., both induced charge on outer and inner surface will redistribute., force on charge q placed inside the cavity will change.

*Multiple options can be correct

QUESTION: 9

Mark the correct options

A.
Gauss’s law is valid only for uniform charge distributions
B.
The flux of the electric field through a closed surface due to all the charges is equal to the flux due to the charges enclosed by the surface
C.
The electric field calculated by Gauss’s law is the field due to all the charges
D.
Gauss’s law is valid only for charges placed in vacuum

Solution:

The correct answers are: The electric field calculated by Gauss’s law is the field due to all the charges, The flux of the electric field through a closed surface due to all the charges is equal to the flux due to the charges enclosed by the surface

*Multiple options can be correct

QUESTION: 10

Two infinite, parallel, non-conducting sheets carry equal positive charge density σ. One is placed in the yz plane at x = 0 and the other at x = a. Take potential V = 0 at x = 0.

Solution:

; (As V_a = 0)

The correct answers are: For potential V_x = 0, For x > a potential

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In front of an earthed conductor a point charge +q is placed as shown in figure :

Two concentric rings of radii R₁ = and R₂ = 4m are placed in yz plane with their centres at origin. They have uniform charge –q and on the inner and outer rings respectively.

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In front of an earthed conductor a point charge +q is placed as shown in figure :

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Two concentric rings of radii R₁ = and R₂ = 4m are placed in yz plane with their centres at origin. They have uniform charge –q and on the inner and outer rings respectively.