Question 295: Magnetism and Matter

Question

A charge of $$4.0 \mu \mathrm{C}$$ is moving with a velocity of $$4.0 	imes 10^6 \mathrm{~ms}^{-1}$$ along the positive $$y$$ axis under a magnetic field $$\vec{B}$$ of strength $$(2 \hat{k}) \mathrm{T}$$. The force acting on the charge is $$x \hat{i} N$$. The value of $$x$$ is __________.

Accepted Answer

$$\begin{aligned}
\mathrm{q} & =4 \mu \mathrm{C}, \overrightarrow{\mathrm{v}}=4 	imes 10^6 \hat{\mathrm{j}} \mathrm{m} / \mathrm{s} \
\overrightarrow{\mathrm{B}} & =2 \hat{\mathrm{k} T} \
\overrightarrow{\mathrm{F}} & =\mathrm{q}(\overrightarrow{\mathrm{v}} 	imes \overrightarrow{\mathrm{B}}) \
& =4 	imes 10^{-6}\left(4 	imes 10^6 \hat{\mathrm{j}} 	imes 2 \hat{\mathrm{k}}ight) \
& =4 	imes 10^{-6} 	imes 8 	imes 10^6 \hat{\mathrm{i}} \
\overrightarrow{\mathrm{F}} & =32 \hat{\mathrm{i}} \mathrm{N} \
\mathrm{x} & =32
\end{aligned}$$

Magnetism and Matter

A charge of $4.0 \mu \mathrm{C} is moving with a velocity of 4.0 \times 10^6 \mathrm{~ms}^{-1} along the positive y axis under a magnetic field \vec{B} of strength (2 \hat{k}) \mathrm{T}. The force acting on the charge is x \hat{i} N. The value of x$ is __________.

Integer / Numeric Answer Type