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GUJCET · Physics · Electrostatic Potential and Capacitance
On the axis and on the equator of an electric dipole for all points ________.
- A on both of them \(V \neq 0\)
- B on both of them \(V =0\)
- C on the axis \(V =0\) and on equator \(V \neq 0\)
- D on the axis \(V \neq 0\) and on equator \(V =0\)
Answer & Solution
Correct Answer
(D) on the axis \(V \neq 0\) and on equator \(V =0\)
Step-by-step Solution
Detailed explanation
(D)
potential due to dipole
\(V (r)=\frac{1}{4 \pi \varepsilon_0} \frac{p \cos \theta}{r^2}\)
on \(\operatorname{axis} \theta=0\) or \(\pi\)
\(\therefore V = \pm \frac{1}{4 \pi \varepsilon_0} \frac{p}{r^2}\)
\(\begin{array}{l}\text { on equator } \theta=\frac{\pi}{2} \\ \therefore V=0\end{array}\)
potential due to dipole
\(V (r)=\frac{1}{4 \pi \varepsilon_0} \frac{p \cos \theta}{r^2}\)
on \(\operatorname{axis} \theta=0\) or \(\pi\)
\(\therefore V = \pm \frac{1}{4 \pi \varepsilon_0} \frac{p}{r^2}\)
\(\begin{array}{l}\text { on equator } \theta=\frac{\pi}{2} \\ \therefore V=0\end{array}\)
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