A point charge q1 = 4q0 is placed at the origin. Another point charge q2 = -q0 is placed at x = 12 cm. The proton is placed on the x-axis so that the electrostatic force on the proton is zero. In…

Given: q1 = 4q0 at the origin and q2 = -q0 at x = 12 cm. Find: The position of the proton on the x-axis where the net electrostatic force is zero. For zero net force on the proton, the magnitudes of the two electrostatic forces must be equal: k |4q0|r^2 = k |q0|(12-r)^2 Cancel the common factors k and q0: 4r^2 = 1(12-r)^2 Taking square root, 2r = 112-r Cross-multiplying, 2(12-r) = r 24 - 2r = r 3r = 24 r = 8 cm Thus, the proton is at a distance 12 + r = 24 cm from the origin. Therefore, the position of the proton from the origin is 24.

A point charge q1 = 4q0 is placed at the origin. Another point ch… — Solution | JEE Physics

NVAMediumJEE 2023Coulomb's Law & Superposition Principle

A point charge $q_1 = 4q_0$ is placed at the origin. Another point charge $q_2 = -q_0$ is placed at $x = 12 \, \text{cm}$ . The proton is placed on the $x$ -axis so that the electrostatic force on the proton is zero. In this situation, the position of the proton from the origin is — $\text{cm}$ .

Answer

Correct answer:24

Step-by-step solution

Standard Method

Given: $q_1 = 4q_0$ at the origin and $q_2 = -q_0$ at $x = 12 \, \text{cm}$ .

Find: The position of the proton on the $x$ -axis where the net electrostatic force is zero.

For zero net force on the proton, the magnitudes of the two electrostatic forces must be equal:

\frac{k \cdot |4q_0|}{r^2} = \frac{k \cdot |q_0|}{(12-r)^2}

Cancel the common factors $k$ and $q_0$ :

\frac{4}{r^2} = \frac{1}{(12-r)^2}

Taking square root,

\frac{2}{r} = \frac{1}{12-r}

Cross-multiplying,

2(12-r) = r

24 - 2r = r

3r = 24

r = 8 \, \text{cm}

Thus, the proton is at a distance

12 + r = 24 \, \text{cm}

from the origin.

Therefore, the position of the proton from the origin is $24$ .

Common mistakes

Taking the distance from the origin directly as $r = 8 \, \text{cm}$ is incorrect because in the working, $r$ is measured from the charge at $x = 12 \, \text{cm}$ in the final placement step. Always interpret the distance definition carefully before concluding the answer.
Placing the proton between the two charges without checking force directions is wrong. Between a positive charge and a negative charge, both forces on the proton act in the same direction there, so they cannot cancel. Check directions before writing the balance equation.
Dropping the modulus of charge magnitudes in the force-balance equation can lead to sign confusion. For balancing magnitudes, use Coulomb-force magnitudes first, then use direction separately to identify the valid region.

Practice more Coulomb's Law & Superposition Principle questions

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

Start free trial More on Coulomb's Law & Superposition Principle

Answer

Step-by-step solution

Common mistakes

Practice more Coulomb's Law & Superposition Principle questions

Related questions