| A charged particle of mass 'm' and charge 'q' moving under the influence of uniform electric field \[E\hat{i}\]and a uniform magnetic field \[B\hat{k}\] follows a trajectory from point P to Q as shown in figure. |
| The velocities at P and Q are respectively, \[v\vec{i}\]and\[-2v\hat{j}\]. Then which of the following statements (A, B, C, D) are the correct? |
| (Trajectory shown is schematic and not to scale) |
 |
| A. \[E=\frac{3}{4}\left( \frac{m{{v}^{2}}}{qa} \right)\] |
| B. Rate of work done by the electric field at P is \[\frac{3}{4}\left( \frac{m{{v}^{3}}}{a} \right)\] |
| C. Rate of work done by both the fields at Q is zero |
| D. The difference between the magnitude of angular momentum of the particle at P and Q is 2 mav. |
| [JEE MAIN Held on 09-01-2020 Morning] |
A) A, B, C
B) A, C, D
C) A, B, C, D
D) B, C, D
Correct Answer: A
Solution :
| [a] \[{{W}_{T}}=\Delta KE\] |
| \[{{W}_{m}}+{{W}_{E}}=\frac{1}{2}m{{\left( 2v \right)}^{2}}-\frac{1}{2}m{{v}^{2}}\] |
| \[0+qE\left( 2a \right)=\frac{3}{2}m{{v}^{2}}\] |
| \[\Rightarrow E=\frac{3}{4}\frac{m{{v}^{2}}}{qa}\] |
| \[\vec{L}_{i}^{o}=mva\left( -\hat{k} \right)\] |
| \[\vec{L}_{f}^{o}=4mva\left( -\hat{k} \right)\] |
| \[\left| \overrightarrow{\Delta {{L}^{o}}} \right|=3mva\] |
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