# Physics Class 12 NCERT Solutions: Chapter 5 Magnetism and Matter Part 8

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Q: 21. A magnetic dipole is under the influence of two magnetic fields. The angle between the field directions is , and one of the fields has a magnitude of . If the dipole comes to stable equilibrium at an angle of with this field, what is the magnitude of the other field?

Answer:

Magnitude of one of the magnetic field,

Magnitude of the other magnetic field

Angle between the two fields

At stable equilibrium, the angle between the dipole and field

Angle between the dipole and field

At rotational equilibrium, the torques between both the fields must balance each other.

∴Torque due to field Torque due to field

Where,

Magnetic moment of the dipole

Hence, the magnitude of the other magnetic field is.

Hence, the magnitude of the other magnetic field is.

Q: 22. A monoenergetic electron beam initially in the horizontal direction is subjected to a horizontal magnetic field of normal to the initial direction. Estimate the up or down deflection of the beam over a distance of. [Note: Data in this exercise are so chosen that the answer will give you an idea of the effect of earth’s magnetic field on the motion of the electron beam from the electron gun to the screen in a TV set.]

Answer:

Energy of an electron beam,

Charge on an electron,

Magnetic field,

Mass of an electron,

Distance up to which the electron beam travels,

We can write the kinetic energy of the electron beam as:

The electron beam deflects along a circular path of radius .

The force due to the magnetic field balances the centripetal force of the path.

Let the up and down deflection of the electron beam be

Where,

Angle of declination

And

Therefore, the up and down deflection of the beam is.