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