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Potential and Field of a Point Charge
Concepts tested here
- Relation between potential and field of a point charge
All Questions
2008 AIPMT 1 question
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The electric potential at a point in free space due to a charge $Q$ coulomb is $Q \times 10^{11}$ volts. The electric field at that point is -For a point charge: $V = \dfrac{Q}{4\pi\varepsilon_0 r}$ and $E = \dfrac{Q}{4\pi\varepsilon_0 r^2}$
Given $V = Q \times 10^{11} = \dfrac{Q}{4\pi\varepsilon_0 r}$
$\Rightarrow r = \dfrac{1}{4\pi\varepsilon_0 \times 10^{11}}$
Dividing the two expressions: $E = \dfrac{V}{r}$
$E = Q \times 10^{11} \times 4\pi\varepsilon_0 \times 10^{11}$
$E = 4\pi\varepsilon_0 Q \times 10^{22}$ volt m$^{-1}$