Chapter 26, Problem 35A

To determine

To find: The magnetic field experienced by an electron moving in an electric field.

Answer to Problem 35A

The required magnetic field experienced by the electron to un-deflected the path is $0.16{\text{Wb/m}}^{\text{2}}$ .

Explanation of Solution

Given:

The velocity of the electron is $3.6\times {10}^6\text{m/s}$

The electric field strength is $\text{5}\text{.8}\times {\text{10}}^5\text{V/m}$

Formula:

The velocity of an electron in the presence of an electric field and the magnetic field is

  $v=\frac{E}{B}$    ......(1)

Here, $v$ is the velocity of the electron, $E$ is the electric field strength and $B$ is the magnetic field strength.

Calculation:

Substitute $3.6\times {10}^6\text{m/s}$ for velocity $\left(v\right)$ and $\text{5}\text{.8}\times {\text{10}}^5\text{V/m}$ for the electric field $(E)$ in equation (1).

  $\begin{array}{c}v=\frac{E}{B}\\ B=\frac{E}{v}\\ =\frac{\text{5}\text{.8}\times {\text{10}}^5\text{V/m}}{3.6\times {10}^6\text{m/s}}\\ =0.16{\text{Wb/m}}^{\text{2}}\end{array}$

Conclusion:

Hence, the required magnetic field experienced by the electron to un-deflected the path is $0.16{\text{Wb/m}}^{\text{2}}$ .