2 concentric spheres of radius R & 2R have charges Q & 2Q.The potential at point P , situated at a point 3R/2 distance from common centre is V , now outer sphere is earthed , the potential at point P now is??/

To solve the problem of finding the potential at point P after the outer sphere is earthed, we need to analyze the situation step by step. We have two concentric spheres: the inner sphere with radius R and charge Q, and the outer sphere with radius 2R and charge 2Q. Initially, the potential at point P, located at a distance of 3R/2 from the common center, is given as V. When the outer sphere is earthed, its potential becomes zero, which will affect the potential at point P.

Understanding the Initial Setup

First, let's calculate the potential at point P before the outer sphere is earthed. The potential due to a charged sphere at a distance greater than its radius can be treated as if all its charge were concentrated at its center. Therefore, the total potential at point P is the sum of the potentials due to both spheres.

Calculating Initial Potential at Point P

• The potential due to the inner sphere (radius R, charge Q) at a distance of 3R/2 is given by:

V_inner = k * Q / (3R/2) = (2kQ) / 3R

• The potential due to the outer sphere (radius 2R, charge 2Q) at the same distance is:

V_outer = k * (2Q) / (3R/2) = (4kQ) / 3R

Thus, the total potential V at point P before earthing the outer sphere is:

V = V_inner + V_outer = (2kQ) / 3R + (4kQ) / 3R = (6kQ) / 3R = 2kQ / R

Effect of Earthing the Outer Sphere

When the outer sphere is earthed, it is connected to the ground, which means its potential is set to zero. This action will redistribute the charge on the outer sphere. The charge on the outer sphere will adjust until its potential becomes zero.

New Potential Calculation

After earthing, the outer sphere will have a new charge, which we can denote as Q_outer. The potential due to the outer sphere at point P will now be:

V_outer_new = k * Q_outer / (3R/2)

Since the outer sphere is earthed, we set this potential to zero:

0 = k * Q_outer / (3R/2) ⇒ Q_outer = 0

This means that the outer sphere effectively has no contribution to the potential at point P after being earthed.

Final Potential at Point P

Now, the potential at point P is solely due to the inner sphere:

V_new = V_inner = (2kQ) / 3R

Conclusion

After the outer sphere is earthed, the potential at point P becomes:

V_new = (2kQ) / 3R

This shows how earthing the outer sphere influences the overall electric potential in the region, demonstrating the importance of grounding in electrical systems.