Question 270: Magnetism and Matter

Question

1 μC charge moving with velocity $\vec{v} = (\hat{i} - 2\hat{j} + 3\hat{k})$ m/s in the region of magnetic field $\vec{B} = (2\hat{i} + 3\hat{j} - 5\hat{k})$ T. The magnitude of force acting on it is $\sqrt{\alpha} 	imes 10^{-6}$ N. The value of $\alpha$ is _______.

Accepted Answer

$$\begin{aligned}
&	ext { Since velocity of light in terms of } \mu \& E 	ext { is }\
&\begin{aligned}
& V=\frac{1}{\sqrt{\mu \epsilon}}=\frac{1}{\sqrt{\mu_0 \mu_{\mathrm{r}}}} 	imes \frac{1}{\sqrt{\epsilon_0 \epsilon_{\mathrm{r}}}} \
& =\frac{1}{\sqrt{\mu_{\mathrm{r}} \epsilon_{\mathrm{r}}}} 	imes \frac{1}{\sqrt{\mu_0 \epsilon_0}} \
& =\frac{C}{\sqrt{\mu_{\mathrm{r}} \epsilon_{\mathrm{r}}}}=\frac{C}{\sqrt{\frac{10}{\pi} 	imes \frac{1}{0.0885}}} \
& =\frac{C}{\sqrt{36}}=\frac{C}{6}
\end{aligned}
\end{aligned}$$
$$\begin{aligned}
V & =\frac{C}{6} \
C & =6 V
\end{aligned}$$
Velocity of light in vacuum is greater by 6 times the velocity of light in medium
Answer is 6

Magnetism and Matter

1 μC charge moving with velocity \vec{v} = (\hat{i} - 2\hat{j} + 3\hat{k}) m/s in the region of magnetic field \vec{B} = (2\hat{i} + 3\hat{j} - 5\hat{k}) T. The magnitude of force acting on it is \sqrt{\alpha} \times 10^{-6} N. The value of \alpha is _______.

Integer / Numeric Answer Type