The electric potential at a point in free space due to a charge Q coulomb is Q × 10^11 volts. The electric field at that point is ?
(a) \( 4\pi \varepsilon_0 Q \times 10^{22} \, \text{volt/m} \)
(b) \( 12\pi \varepsilon_0 Q \times 10^{20} \, \text{volt/m} \)
(c) \( 4\pi \varepsilon_0 Q \times 10^{20} \, \text{volt/m} \)
(d) \( 12\pi \varepsilon_0 Q \times 10^{22} \, \text{volt/m} \)
Answer : (a) \( 4\pi \varepsilon_0 Q \times 10^{22} \, \text{volt/m} \)
\[ E = \dfrac{kQ}{r^2} \]
\( V = \dfrac{kQ}{r} = Q \times 10^{11} \) \( \Rightarrow \dfrac{Q}{r} = 4\pi \varepsilon_0 Q \times 10^{11} \\ \)
\( E = \dfrac{Q \times 10^{11}}{r} \\ \)
\( = 4\pi \varepsilon_0 Q \times 10^{11} \times 10^{11} \\ \)
\( = 4\pi \varepsilon_0 Q \times 10^{22} \)
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