The distance between two charges $ q_1 = +2 \, \mu C $ and $ q_2 = +8 \, \mu C $ is 15 cm. Calculate the distance from the charge $ q_1 $ to the points on the line segment joining the two charges where the electric field is zero.

Question

There are three co-centric conducting spherical shells $A$, $B$ and $C$ of radii $a$, $b$ and $c$ respectively $(c>b>a)$ and they are charged with charges $q_1$, $q_2$ and $q_3$ respectively. The potentials of the spheres $A$, $B$ and $C$ respectively are:

Answer 1

Step 1: Understanding the Concept
The "neutral point" is the location where the electric fields produced by the two charges are equal in magnitude but opposite in direction, resulting in a net field of zero.
Step 2: Key Formula or Approach
Let the distance from $q_1$ be $x$. The distance from $q_2$ will be $(15 - x)$. At the neutral point: \[ E_1 = E_2 \implies \frac{k q_1}{x^2} = \frac{k q_2}{(15-x)^2} \]
Step 3: Detailed Calculation
1. Substitute the values: \[ \frac{2}{x^2} = \frac{8}{(15-x)^2} \] 2. Simplify the ratio: \[ \frac{1}{x^2} = \frac{4}{(15-x)^2} \] 3. Take the square root of both sides: \[ \frac{1}{x} = \frac{2}{15-x} \] 4. Cross-multiply and solve for $x$: \[ 15 - x = 2x \implies 15 = 3x \implies x = 5 \text{ cm} \]
Step 4: Final Answer
The distance from $q_1$ is 5 cm.

The distance between two charges \( q_1 = +2 \, \mu C \) and \( q_2 = +8 \, \mu C \) is 15 cm. Calculate the distance from the charge \( q_1 \) to the points on the line segment joining the two charges where the electric field is zero.

Show Hint

The Correct Option is

Solution and Explanation

Top Questions on Electrostatics

Questions Asked in KEAM exam