Logo
Jeeify
MCQMediumJEE 2023Electric Field & Field Lines

JEE Physics 2023 Question with Solution

Two equal positive point charges are separated by a distance 2a2a. The distance of a point from the centre of the line joining two charges on the equatorial line (perpendicular bisector) at which force experienced by a test charge q0q_0 becomes maximum is ax\frac{a}{\sqrt{x}}. The value of xx is _____.

  • A

    11

  • B

    22

  • C

    33

  • D

    44

    Diagram of two equal positive charges separated vertically by distance 2a, with a test charge on the perpendicular bisector at distance x from the centre.Small overlay handle image from page widget, not part of the physics diagram, shown beside the extracted option area.

Answer

Correct answer:B

Step-by-step solution

Standard Method

Given: Two equal positive point charges are separated by 2a2a. A test charge q0q_0 is placed on the perpendicular bisector at distance xx from the centre.

Find: The value of xx in ax\frac{a}{\sqrt{x}} for which the force on q0q_0 is maximum.

From the solution, the force is

F=2Kqq0x(x2+a2)3/2F = \frac{2Kqq_0x}{(x^2+a^2)^{3/2}}

For maximum force,

dFdx=0\frac{dF}{dx} = 0

Using the result shown in the solution,

x=a2x = \frac{a}{\sqrt{2}}

Comparing with the given form ax\frac{a}{\sqrt{x}}, we get

x=2x = 2

Therefore, the correct option is B.

Common mistakes

  • Using the force due to only one charge is incorrect because the net force on the test charge is the vector sum of forces due to both equal charges. Resolve components and add the horizontal components properly.

  • Adding the full magnitudes of the two forces directly is wrong because the vertical components cancel on the perpendicular bisector. Only the components along the bisector contribute to the net force.

  • After obtaining a2\frac{a}{\sqrt{2}}, treating it as the final value of the blank is incorrect. The question asks for the value of xx in the form ax\frac{a}{\sqrt{x}}, so compare the forms to get x=2x=2.

Practice more Electric Field & Field Lines questions

Get unlimited AI-adaptive practice, mastery tracking, and an AI tutor that explains every step — free to start.

Start free trialMore on Electric Field & Field Lines

Related questions