SATHEE: Electrostatics Question 214

Electrostatics Question 214

Question: Equal charges $q$ are placed at the four corners $A, B, C, D$ of a square of length $a$ . The magnitude of the force on the charge at B will be [MP PMT 1994; DPMT 2001]

Options:

A) $\frac{3 q^{2}}{4 π ε_{0} a^{2}}$

B) $\frac{4 q^{2}}{4 π ε_{0} a^{2}}$

C) $(\frac{1 + 2 \sqrt{2}}{2}) \frac{q^{2}}{4 π ε_{0} a^{2}}$

D) $(2 + \frac{1}{\sqrt{2}}) \frac{q^{2}}{4 π ε_{0} a^{2}}$

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Answer:

Correct Answer: D

Solution:

After following the guidelines mentioned above $F_{n e t} = F_{A C} + F_{D} = \sqrt{F_{A}^{2} + F_{C}^{2} +} F_{D}$ Since $F_{A} = F_{C} = \frac{k q^{2}}{a^{2}}$ and $F_{D} = \frac{k q^{2}}{{(a \sqrt{2})}^{2}}$

$F_{n e t} = \frac{\sqrt{2} k q^{2}}{a^{2}} + \frac{k q^{2}}{2 a^{2}} = \frac{k q^{2}}{a^{2}} (\sqrt{2} + \frac{1}{2})$

$= \frac{q^{2}}{4 π ε_{0} a^{2}} (\frac{1 + 2 \sqrt{2}}{2})$

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Electrostatics Question 214

Question: Equal charges q are placed at the four corners A,B,C,D of a square of length a . The magnitude of the force on the charge at B will be [MP PMT 1994; DPMT 2001]

Options:

Answer:

Solution:

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Question: Equal charges $q$ are placed at the four corners $A, B, C, D$ of a square of length $a$ . The magnitude of the force on the charge at B will be [MP PMT 1994; DPMT 2001]