Chapter 27, Problem 1P

To determine

The value of $e/m$.

Answer to Problem 1P

Solution:

The value of $e/m$ is $6.2\times {10}^4\text{C/kg}$.

Explanation of Solution

Given:

Radius of the circle, $r=14\text{mm}=\text{0}\text{.014}\text{m}$

Magnetic field, $B=0.86\text{T}$

Electric field, $E=640\text{V/m}$

Formula used:

The value of $e/m$ is calculated by the formula

$\frac{e}{m}=\frac{E}{B^{2}r}$

Here,

$E$ is the electric field

$B$ is the magnetic field

$r$ is the radius

Solution:

The value of $e/m$ is calculated as

$\frac{e}{m}=\frac{E}{B^{2}r}$

Plugging the values in the above equation

$\begin{array}{c}\frac{e}{m}=\frac{640}{{0.86}^2\times 0.014}\\ =6.1809\times {10}^4\text{C/kg}\\ =\text{6}\text{.2}\times {\text{10}}^4\text{C/kg}\end{array}$

Conclusion:

The value of $e/m$ is $6.2\times {10}^4\text{C/kg}$.