Question

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?

Answer 1

9.762 × 10⁻¹² N

Step-by-step 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