Question

An electron flies into a homogeneous magnetic field perpendicular to the field lines. The velocity of the electron is $v=4\times {10}^7\text{m/s}$. The induction of the field is ${10}^{-3}\text{T}$. The acceleration of the electron in the magnetic field is approximately -

• A. $7\times {10}^{15}{\text{m/s}}^2$
• B. $7\times {10}^{13}{\text{m/s}}^2$
• C. $7\times {10}^{14}{\text{m/s}}^2$
• D. $7\times {10}^{10}{\text{m/s}}^2$

Answer 1

The correct option is A $7\times {10}^{15}{\text{m/s}}^2$

Given:
Velocity of electron, $v=4\times {10}^7\text{m/s}$
Magnetic field, $B={10}^{-3}\text{T}$
Mass of electron, $m=9.1\times {10}^{-31}\text{kg}$

Acceleration,

$a=\frac{F_m}{m}=\frac{qvB\sin \theta }{m}$

Substituting the values,

$a=\frac{1.6\times {10}^{-19}\times 4\times {10}^7\times {10}^{-3}\times \sin {90}^{\circ }}{9.1\times {10}^{-31}}$

$\therefore a\approx 7\times {10}^{15}{\text{m/s}}^2$

Hence, option $\left(A\right)$ is the correct answer.