Question

An electron starts from rest near a negatively charged metal plate, and is accelerated towards a positive plate through a potential difference of 1320 volts. The electron passes through a hole in the positive plate into a region where the electric field is negligible. Calculate the magnetic field at the location A, a distance of 0.008 meters from the electron, due to the moving electron.

Answer 1

Answer:

The magnetic field at the location is $5.375\times10^{-15}\ T$

Explanation:

Given that,

Potential difference = 1320 V

Distance = 0.008 m

We need to calculate the velocity

Using conservation of energy

Electric potential energy lost = kinetic energy gained

$qV=\dfrac{1}{2}mv^2$

$v^2=\dfrac{2qV}{m}$

Put the value into the formula

$v^2=\dfrac{2\times1.6\times10^{-19}\times1320}{9.1\times10^{-31}}$

$v=\sqrt{\dfrac{2\times1.6\times10^{-19}\times1320}{9.1\times10^{-31}}}$

$v=2.15\times10^{7}\ m/s$

We need to calculate the magnetic field at the location

Using formula of magnetic field

$B=\dfrac{\mu qv}{4\pi r^2}$

Put the value into the formula

$B=\dfrac{4\pi\times10^{-7}\times1.6\times10^{-19}\times2.15\times10^{7}}{4\pi\times(0.008)^2}$

$B=5.375\times10^{-15}\ T$

Hence, The magnetic field at the location is $5.375\times10^{-15}\ T$