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*Multiple options can be correct

QUESTION: 1

A Positive point charge is moving in clockwise direction in a circle with constant speed. Consider the magnetic field produced by the charge at a point ** P** (not centre of the circle) on the axis of the circle. Which of the following is incorrect.

Solution:

The point charge moves in circle as shown in figure. The magnetic field vectors at a point ** P** on axis of circle are at the instants the point charge is at

Hence as the particles rotates in circle, only magnitude of magnetic field remains constant at the point on axis ** P** but its direction changes.

The correct answers are: it is constant in direction only, it is constant in direction and magnitude both, it is not constant in magnitude and direction both.

*Multiple options can be correct

QUESTION: 2

The negatively and uniformly charged nonconducting disc as shown in the figure is rotated clockwise with great angular speed. Which of the following is not the direction of the magnetic field at point ** A** in the plane of the disc :

Solution:

Disc behaves like made up of coils arranged in a plane in which current is flowing in anti-clockwise direction.

Hence, the field at ** A** is direction into the page.

The correct answers are: out of the page, up the page, down the page

*Multiple options can be correct

QUESTION: 3

In a region magnetic field along x-axis changes with time according to the given graph. If time period, pitch and radius of helix path are T_{0}, P_{0} and R respectively then which of the following is correct if the particle is projected at an angle θ_{0} with the positive x-axis in x-y plane.

Solution:

As the magnetic field is along the *x*-axis, the magnetic force will be along negative *z*-axis from ** t = 0** to

** t = T_{0}** to

For

At

*y*-coordinate = 0 (from figure)

and *z*-coordinate = **–2 R_{0}** (from figure)

The correct answers are: At co-ordinates of charge are co-ordinates of charge are Two extremes from *x*-axis are at a distance **2 R_{0}** from each other.

*Multiple options can be correct

QUESTION: 4

Three infinite current carrying conductors are placed as shown in figure. Two wires carry same current while current in third wire is unknown. The three wires do not intersect with each other and all of them are in the plane of paper. Which of the following is incorrect about a point ** ‘P’** which is also in the same plane :

Solution:

Magnetic field at ** ‘P’** due to wires (1) and (2) is :

(out of the paper)

The correct answers are: Magnetic field intensity at ** P** is zero for all values of

*Multiple options can be correct

QUESTION: 5

From a cylinder of radius ** R**, a cylinder of radius

Solution:

For cylinder

We can consider the given cylinder as a combination of two cylinders. One of radius ** ‘R’** carrying current.

The correct answers are:

*Multiple options can be correct

QUESTION: 6

A nonconducting disc having uniform positive charge ** Q**, is rotating about its axis in anticlockwise direction with uniform angular velocity ω. The magnetic field at the center of the disc is.

Solution:

Consider a ring of radius ** x** and thickness

Equivalent current in this ring

** dB** (due to this ring)

The correct answers are: directed outward, having magnitude

*Multiple options can be correct

QUESTION: 7

A long thick conducting cylinder of radius ** ‘R’** carries a current uniformly distributed over its cross section.

Solution:

**Alterante solution**

*B* (inside the conductor) ∝ r, *B*(outside the conductor)

The correct answers are: The magnetic field strength is maximum on the surface, The energy density of the magnetic field outside the conductor varies as inversely proportional to **1/ r^{2}**, where

*Multiple options can be correct

QUESTION: 8

A charge particle of charge ** q**, mass

Solution:

The correct answers are: Velocity of particle when it comes out from magnetic field is Time for which the particle was in magnetic field is Distance traveled in magnetic field is

*Multiple options can be correct

QUESTION: 9

If a charged particle of charge to mass ratio q/m = α is entering in a uniform magnetic field of strength ** B** which is extended up to 4

Solution:

Electromagnetic force will provide the necessary centripetal force.

⇒

*i.e*. the electron will move out after traveling on a semicircular path of radius ** r = 2d**.

The correct answers are: angle subtended by charged particle at the centre of circular path is 2π, the time for which particle will be in the magnetic field is the charged particle will subtended an angle of 90° at the centre of circular path

*Multiple options can be correct

QUESTION: 10

A particle of charge ** ‘q’** and mass

Solution:

The particle will move along an arc which is part of a circle of radius

From the figure we can see *r* =**R**

The correct answers are:

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