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QPages 121-124: Q73: HC Verma: Concepts of Physics - Volume 2 Electric Field Potential Pages 121-124: Q73 Solution: Find the magnitude of the electric field at the point P in the…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often replace $(d^2+a^2)^{3/2}$ with $d^3+a^3$ or drop the $a^2$ term outright, yielding an incorrect coefficient for the dipole contribution. Use the binomial series: $(d^2+a^2)^{-3/2}=d^{-3}(1+(a/d)^2)^{-3/2}\approx d^{-3}\big[1-\frac32(a/d)^2\big]$, so the leading dipole term is $3kqa/d^3$, not $2kqa/d^3$ or $kqa/d^3$.

Find the magnitude of the electric field at the point P in the configuration shown in the figure for

d \gg a

.

Step-by-Step Verified Solution

**Answer:**

E = \frac{3kqa}{(d^2 + a^2)^{3/2}} + \frac{kq}{d^2}

(for

d \gg a

,

E \approx \frac{kq}{d^2} + \frac{3kqa}{d^3}

). **STEP-BY-STEP Explanation:** The configuration consists of a charge

q

and a dipole. The field is the sum of the field due to the charge and the field due to the dipole .

All Questions in this Chapter

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