KCET · Physics · Electrostatics
The electric field and the potential of an electric dipole vary with distance \(r\) as
- A \(\frac{1}{r^2}\) and \(\frac{1}{r}\)
- B \(\frac{1}{r^2}\) and \(\frac{1}{r^3}\)
- C \(\frac{1}{r^3}\) and \(\frac{1}{r^2}\)
- D \(\frac{1}{r}\) and \(\frac{1}{r^2}\)
Answer & Solution
Correct Answer
(C) \(\frac{1}{r^3}\) and \(\frac{1}{r^2}\)
Step-by-step Solution
Detailed explanation
We know electric field and potential due to electric dipole on axial position is given as
\(E=\frac{1}{4 \pi \varepsilon_0} \frac{2 p}{r^3} \text { and } V=\frac{1}{4 \pi \varepsilon_0} \frac{p}{r^2}\)
i.e. \(E \propto \frac{1}{r^3}\) and \(V \propto \frac{1}{r^2}\)
\(E=\frac{1}{4 \pi \varepsilon_0} \frac{2 p}{r^3} \text { and } V=\frac{1}{4 \pi \varepsilon_0} \frac{p}{r^2}\)
i.e. \(E \propto \frac{1}{r^3}\) and \(V \propto \frac{1}{r^2}\)
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