Question

Calculated the kinetic energy of a point charge of $6\mu C$ at $x = 3m$ which was initially at rest at the origin. A uniform electric field of $4kN{C^{ - 1}}$ exists in $x$ direction.
A) $ - 24mJ$
B) $ - 72mJ$
C) $24mJ$
D) $72mJ$

Answer 1

Hint: Firstly we have to figure out all the known quantities for the given question ( In this case the charge, point and the electric field).Then we have to use the aspect for force to compare and obtain the value for the acceleration in terms of electric field and charge. Then we can replicate it in a formula for energy and obtain a desired formula for the kinetic energy and obtain an answer by solving it .


Complete step by step answer:
Firstly we have to sort out what we have got :
Kinetic energy of the point charge : $6\mu C$
Point at which it exist : $x = 3m$
Value of the Electric field : $4kN{C^{ - 1}}$
Step 1: We have to define the presumed acceleration be $a$ and then use the aspect of force to compare it and find the formula for the acceleration for the given problem :
$
  F = eE{\text{ & }}F = ma \\
  therefore, \\
  eE = ma \\
  \dfrac{{eE}}{m} = a \\
 $
Step 2: Now we just have to use this value in the formula for Kinetic energy to obtain a certain formula in its terms(Work done by the electric field is change in kinetic energy of particle):
$\dfrac{1}{2}m{v^2} = eEx$
Step 3: we just have to put the value in the equation to get the kinetic energy :
$
  K = eEx \\
  \Rightarrow K = 4 \times {10^3} \times 6 \times {10^{ - 6}} \times 3 \\
  \Rightarrow K = 72 \times {10^{ - 3}}J \\
  \Rightarrow K = 72mJ \\
 $
Hence the correct option is option D, $72mJ$ .

Note: The given formula is only valid for the point charge, if we increase the diameter and make the sizes comparable then it will change the entire concept. Then we have to use integrative methods to obtain the formulas and the answers.