A neutral solid conducting sphere of radius R has charge Q deposited in it, and is sitting at the centre of a conducting shell of inner radius 2R and outer radius 3R. After the conductor reaches equilibrium, find the potential at R<r<2R at r=R, and at r=R/2, and r=5/2R.
To find the potential at different points within the conducting shell, we need to consider two conditions: (1) inside the solid conducting sphere, and (2) inside the conducting shell but outside the solid sphere.
1. Inside the solid conducting sphere (r < R):
The potential at any point inside a uniformly charged solid sphere can be found using the formula:
V = k * (Q / R)
where V is the potential, k is the electrostatic constant, Q is the charge, and R is the radius of the sphere. In this case, the potential will be the same throughout the solid sphere since it is a conductor at equilibrium.
2. Inside the conducting shell but outside the solid sphere (R < r < 2R):
The potential at any point within a conducting shell resulting from an inner charge can be found using the formula:
V = k * (Q / r)
where V is the potential, k is the electrostatic constant, Q is the charge, and r is the distance from the center of the conducting shell. In this case, the charge responsible for the potential is the charge deposited in the solid conducting sphere, Q.
Now, let's calculate the potentials at the given points:
a) At r = R:
Inside the solid conducting sphere (r < R), the potential is given by:
V = k * (Q / R)
b) At r = R/2:
Inside the conducting shell but outside the solid sphere (R < r < 2R), the potential is given by:
V = k * (Q / r)
Simply plug in the values to find the potential at this point.
c) At r = 5/2R:
Inside the conducting shell but outside the solid sphere (R < r < 2R), the potential is given by:
V = k * (Q / r)
Again, plug in the values to find the potential at this point.
Note: Remember to use consistent units for the radius (R) and charge (Q) in the calculations.