Q159 / 180 · COMEDK 2024 (Memory Based) · Physics
An electron is moving along positive $X$-axis. To get it moving on an anti-clockwise circular path in $X-Y$-plane, a magnetic field is applied
- Aalong positive $Y$-axis
- Correct answerBalong positive $Z$-axis
- Calong negative $Y$-axis
- Dalong negative $Z$-axis
Solution
For the particle to move along anti-clockwise path, force should be along $\hat{\mathbf{j}} y$-direction.
Since, velocity is along $\hat{\mathbf{i}}$,
Hence, $F_m=-e(\mathbf{v} \times \mathbf{B})$
In terms of unit vectors,
$\begin{aligned}<br/>& \hat{\mathbf{j}}=-(\hat{\mathbf{i}} \times \hat{\mathbf{p}}) \\<br/>\Rightarrow \quad & \hat{\mathbf{j}}=\hat{\mathbf{p}} \times \hat{\mathbf{i}}<br/>\end{aligned}$
Clearly, $\hat{\mathbf{p}}=\hat{\mathbf{k}}$
Hence, magnetic field is applied along positive Z -axis.
Since, velocity is along $\hat{\mathbf{i}}$,
Hence, $F_m=-e(\mathbf{v} \times \mathbf{B})$
In terms of unit vectors,
$\begin{aligned}<br/>& \hat{\mathbf{j}}=-(\hat{\mathbf{i}} \times \hat{\mathbf{p}}) \\<br/>\Rightarrow \quad & \hat{\mathbf{j}}=\hat{\mathbf{p}} \times \hat{\mathbf{i}}<br/>\end{aligned}$
Clearly, $\hat{\mathbf{p}}=\hat{\mathbf{k}}$
Hence, magnetic field is applied along positive Z -axis.
Hence, the correct answer is option: 'B'.