A) \[qE{{y}^{2}}\]
B) \[q{{E}^{2}}y\]
C) \[qEy\]
D) \[{{q}^{2}}Ey\]
Correct Answer: C
Solution :
| [c] Key Idea: Kinetic energy obtained by the particle is equal to the work done in moving a distance y. |
| Electric force on charged particle |
| \[F=qE\] |
| Kinetic energy attained by particle |
| = work done |
| = force \[\times \] displacement |
| \[=qE\times y\] |
| Alternative: |
| Force on charged particle in a uniform electric field is |
| \[F=ma=Eq\] |
| or \[a=\frac{Eq}{m}\] (i) |
| From the equation of motion, we have |
| \[{{v}^{2}}={{u}^{2}}+2ay\] |
| \[=0+2\times \frac{Eq}{m}\times y\] |
| \[=\frac{2Eqy}{m}\] |
| Now kinetic energy of the particle |
| \[K=\frac{1}{2}m{{v}^{2}}\] |
| \[=\frac{m}{2}\times \frac{2\,E\,qy}{m}=qEy\] |
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