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GUJCET · Physics · Electric Charges and Fields
Electrical field intensity due to an electric dipole on its axis at distance x \((x \gg a)\) and on the equatorial at distance y \((y \gg a)\) are same. what is the ratio of x and y ?
- A \(\sqrt{2}: 1\)
- B \(1: \sqrt[3]{2}\)
- C \(\sqrt[3]{2}: 1\)
- D \(1: 2\)
Answer & Solution
Correct Answer
(C) \(\sqrt[3]{2}: 1\)
Step-by-step Solution
Detailed explanation
(C)
\(\begin{aligned} \mid E \text { axis } \mid & =\mid E \text { equator } \mid \\ \frac{2 k p}{x^3} & =\frac{k p}{y^3} \\ \therefore \quad \frac{x^3}{y^3} & =\frac{2}{1} \\ \therefore \quad \frac{x}{y} & =\frac{\sqrt[3]{2}}{1}\end{aligned}\)
\(\begin{aligned} \mid E \text { axis } \mid & =\mid E \text { equator } \mid \\ \frac{2 k p}{x^3} & =\frac{k p}{y^3} \\ \therefore \quad \frac{x^3}{y^3} & =\frac{2}{1} \\ \therefore \quad \frac{x}{y} & =\frac{\sqrt[3]{2}}{1}\end{aligned}\)
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