An electron in a vacuum is first accelerated by a voltage of 79900 V and then enters a region in which there is a uniform magnetic field of 0.364 T at right angles to the direction of the electron's motion. What is the force on the electron due to the magnetic field?

9.762 * 10⁻¹² N

Explanation:

Given:

Voltage, V = 79900 Volts

Magnetic field, B = 0.364 T

Now,

The energy (E) due to the applied potential difference,

E = eV

where,

e is the charge of the electron = 1.6 * 10⁻¹⁹ C

thus,

E = 1.6 * 10⁻¹⁹ * 79900 J

also,

kinetic energy due to the applied potential

K. E = (1/2) mv²

where, m is the mass of the electron

v is the velocity of the electron

also

E = K. E

thus we have

1.6 * 10⁻¹⁹ * 79900 J = (1/2) * 9.1 * 10⁻³¹ * v²

or

v = 1.676 * 10⁸ m/s

therefore,

The force in the electron, F = evB

or

F = 1.6 * 10⁻¹⁹ * 1.676 * 10⁸ * 0.364

or

F = 9.762 * 10⁻¹² N