185k views
4 votes
An electron having energy 10ev is circulating in path having magnetic field of 10⁻⁴t. the speed of the electron is

A. 11 cm

B. 18 cm

C. 12 cm

D. 16 cm

1 Answer

3 votes

The speed of the electron is determined as 2.0 x 10⁶ m/s. (Option A).

How to calculate the speed of the electron?

The speed of the electron is calculated by applying the following formula as shown below.

Magnetic force on a charge:

F = qvB

Centripetal force on a charge on circular path;

F = mv²/r

mv²/r = qvB

mv/r = qB

mv = qBr

v = qBr / m

where;

  • m is the mass of electron
  • q is the charge of electron
  • B is magnetic field strength
  • r is the radius of the path

The speed of the electron is calculated as;

v = (1.6 x 10⁻¹⁹ x 10⁻⁴ x 0.1 ) / (9.11 x 10⁻³¹)

v = 1.8 x 10⁶ m/s

v ≈ 2.0 x 10⁶ m/s

The complete question is below:

an electron having energy 10ev is circulating in path of radius 0.1 m, having magnetic field of 10⁻⁴t. the speed of the electron is?

A. 2.0 x 10⁶ m/s

B. 4.8 x 10⁶ m/s

C. 2.0 x 10¹² m/s

D. 4.8 x 10¹² m/s

User Nutritioustim
by
7.7k points