NCERT Physics Class 12 Exemplar Ch 4 Moving Charges and Magnetism Part 5

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Long Answer Types Questions

Q.23 A turn rectangular coil (in plane) is hung from one arm of a balance (Fig.). A mass is added to the other arm to balance the weight of the coil. A current passes through the coil and a constant magnetic field of acting inward (in plane) is switched on such that only arm of length lies in the field. How much additional mass must be added to regain the balance?

Additional mass to gain balance

Additional Mass to Gain Balance

Additional mass to gain balance

Solution:

When the field is off

When the magnetic field is switched on

Q.24 A rectangular conducting loop consists of two wires on two opposite sides of length joined together by rods of length . The wires are each of the same material but with cross-sections differing by a factor of . The thicker wire has a resistance and the rods are of low resistance, which in turn are connected to a constant voltage source V0. The loop is placed in uniform a magnetic field at to its plane. Find , the torque exerted by the magnetic field on the loop about an axis through the centers of rods.

Solution:

Net torque

Q.25 An electron and a positron are released from and respectively, in a uniform magnetic field each with an equal momentum of magnitude . Under what conditions on the direction of momentum will the orbits be nonintersecting circles?

Solution:

As is along the x axis, for a circular orbit the momenta of the two particles are in the plane. Let and be the momentum of the electron and positron, respectively. Both of them define a circle of radius R. They shall define circles of opposite sense. Let make an angle with the axis must make the same angle. The centers of the respective circles must be perpendicular to the momenta and at a distance . Let the center of the electron be at and of the positron at . The coordinates of is

The coordinates of is

The coordinates of is

Coordinates of point

Coordinates of Point

Coordinates of point

The circles of the two shall not overlap if the distance between the two centers are greater than

Let d be the distance between

Then

Since has to be greater than

Or,