Physics Class 12 NCERT Solutions: Chapter 4 Moving Charges and Magnetism Part 6

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Magnetic field of straight wire

Magnetic Field of Straight Wire

Q: 17. A toroid has a core (non-ferromagnetic) of inner radius and outer radius, around which turns of a wire are wound. If the current in the wire is, what is the magnetic field (a) outside the toroid, (b) inside the core of the toroid, and (c) in the empty space surrounded by the toroid.

Answer:

Inner radius of the toroid,

Outer radius of the toroid,

Number of turns on the coil,

Current in the coil,

(A) Magnetic field outside a toroid is zero. It is non-zero only inside the core of a toroid.

(B) Magnetic field inside the core of a toroid is given by the relation,

Where,

Permeability of free space

Length of toroid

(c) Magnetic field in the empty space surrounded by the toroid is zero.

Q: 18. Answer the following questions:

(A) A magnetic field that varies in magnitude from point to point but has a constant direction (east to west) is set up in a chamber. A charged particle enters the chamber and travels undeflected along a straight path with constant speed. What can you say about the initial velocity of the particle?

(B) A charged particle enters an environment of a strong and non-uniform magnetic field varying from point to point both in magnitude and direction, and comes out of it following a complicated trajectory. Would its final speed equal the initial speed if it suffered no collisions with the environment?

(C) An electron travelling west to east enters a chamber having a uniform electrostatic field in north to south direction. Specify the direction in which a uniform magnetic field should be set up to prevent the electron from deflecting from its straight line path.

Answer:

(A) The initial velocity of the particle is either parallel or anti-parallel to the magnetic field. Hence, it travels along a straight path without suffering any deflection in the field.

(B) Yes, the final speed of the charged particle will be equal to its initial speed. This is because magnetic force can change the direction of velocity, but not its magnitude.

(B) An electron travelling from West to East enters a chamber having a uniform electrostatic field in the North-South direction. This moving electron can remain undeflected if the electric force acting on it is equal and opposite of magnetic field. Magnetic force is directed towards the South. According to Fleming’s left hand rule, magnetic field should be applied in a vertically downward direction

Q: 19. An electron emitted by a heated cathode and accelerated through a potential difference of, enters a region with uniform magnetic field of. Determine the trajectory of the electron if the field (A) is transverse to its initial velocity, (B) makes an angle of with the initial velocity.

Answer:

Magnetic field strength,

Charge on the electron,

Mass of the electron,

Potential difference,

Thus, kinetic energy of the electron

Where,

(a) Magnetic force on the electron provides the required centripetal force of the electron. Hence, the electron traces a circular path of radius r.

Magnetic force on the electron is given by the relation,

From equations (1) and (2), we get

Hence, the electron has a circular trajectory of radius normal to the magnetic field.

(B) When the field makes an angle of with initial velocity, the initial velocity will be,

From equation (2), we can write the expression for new radius as:

Hence, the electron has a helical trajectory of radius along the magnetic field direction.

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