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A charge of 10 μC is brought from infinity to point P in an external electric field. Point P is located at a distance of 5 cm away from 5 μC charge. Calculate the work done to bring the 10 μC to point P from infinity? 
1. 90 J
2. 9J
3. 900J
4. 9000 J

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Best answer
Correct Answer - Option 2 : 9J

CONCEPT

  • The amount of work done in moving a unit positive charge in an electric field from infinity to that point without accelerating the charge against the direction of the electric field.
  • The electrostatic potential is given by

\(\Rightarrow V = \frac{W}{q}\)

  • The electrostatic potential due to a point charge is given by 

\(\Rightarrow V = \frac{Kq}{r}\)                                        \([\because K = \frac{1}{4\pi\epsilon_{0}}]\)

Where W = Work , q = charge, and r = distance

CALCULATION :

Given - q1 = 5μC, r = 5cm =5× 10-2 m,q2 = 10μC

  • The electric potential due to 5μC at a distance of 5 cm away from it is 

\(\Rightarrow V = \frac{9\times 10^{9}\times 5\times 10^{-6}}{5\times 10^{-2}} = 9\times 10^{5} V\)

  • The work done in moving the charge of 10 μC from infinity to P is 

\(\Rightarrow W = V\times q = 9\times 10^{5}\times 10\times 10^{-6}=9 J\)

  • Hence option 2 is the answer

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