Chapter 26, Problem 64A

To determine

To Find: The $\frac{q}{m}$ ratio of an accelerated particle.

Answer to Problem 64A

The ratio of $\frac{q}{m}$ is $306.122$ .

Explanation of Solution

Given:

Potential difference $\text{=}\text{1}{\text{.5×10}}^{\text{2}}\text{V}$

Magnetic field $\text{=}50\text{mT}$

Radius of the curved path $\text{=}9.8\text{cm}$

Formula:

The ratio of $\frac{q}{m}$ is given by

  $\frac{q}{m}=\frac{v}{BR}$  ...... (1)

Here $v$ is the velocity of the particle, $B$ is magnetic field applied and $R$ is the radius of curved path.

Calculation:

Substitute $\text{1}{\text{.5×10}}^{\text{2}}\text{V}$ for $v$ , $50\text{mT}$ for $B$ and $9.8\text{cm}$ for $R$ in equation (1)

  $\begin{array}{c}\frac{q}{m}=\frac{v}{BR}\\ =\frac{1.5\times {10}^2}{50\times {10}^{-3}\times 9.8}\\ =306.122\end{array}$

Conclusion:

Hence, the required ratio of $\frac{q}{m}$ is $306.122$ .