The electric potential at a certain distance from a point charge is 600 V and the electric field is `200 NC^(-1)`. Which of the following statements will be true?

Options

A. The magnitude of the charge is `20 xx 10^(-3)C`.
B. The distance of the given point from the charge is 3 m.
C. The potential at a distance of 9 m will be 200 V.
D. The work done by an external agent in moving a point charge of 1 mC from the given point at a distance of 9 m will be `4 xx 10^(-4) J`.

Answer

B, C

Explanation

b.,c.
`V=(1)/(4piepsilon_(0))(q)/(x)=600` ......(i)
`E=(1)/(4piepsilon_(0))(q)/(x^(2))=200` ......(ii)
From Eq. (i) and Eq. (ii), `x=3m`
From Eq. (i). `q=(600xx3)/(9xx10^(9))=2xx10^(-7)C`
`V'=(1)/(4piepsilon_(0))(q)/(x')=9xx10^(9)xx(2xx10^(-7))/(9)=200V`
`W=q(V]-V)=10^(-6)(200-600)=-4xx10^(-4)J`