Question

A charged conducting spherical shell of radius R = 2 m with total charge q = 61 μC produces the electric field given by Part (a) Enter an expression for the electric potential inside the sphere ( r < R ) in terms of the given quantities, assuming the potential is zero at infinity. Part (b) Calculate the electric potential, in volts, at radius r inside the charged shell.

Answer 1

The electric potential inside a charged conducting spherical shell is zero. Regardless of the value of r, the electric potential inside the shell will always be zero.

Step-by-step explanation:

To find the electric potential inside a charged conducting spherical shell, we can use the fact that for r < R (inside the shell), the electric potential is constant and equal to zero. This is because the electric field inside a conductor is always zero.

So, the expression for the electric potential inside the sphere (r < R) in terms of the given quantities is:

V = 0

To calculate the electric potential at a specific radius r inside the charged shell, we still use the fact that the electric potential inside the shell is constant and equal to zero. So, regardless of the value of r, the electric potential inside the shell will always be zero.

Answer 2

The electric potential inside a charged spherical conductor is constant and equal to the potential on the surface. Given the radius R = 2m and charge q = 61µC, the electric potential at radius r within the spherical shell is 272.5 volts.

Step-by-step explanation:

The subject of the student's question is Physics, and it pertains to the concepts of electric fields and electric potential related to a spherical conductor. For part (a), since the electric field inside a conducting shell is zero, the electric potential is constant throughout the interior of the sphere. By setting the potential to zero at infinity, the potential inside the sphere is simply the potential on the surface, which is given by V = kq/R, where k is Coulomb's constant, q is the total charge on the sphere, and R is the radius of the sphere.

For part (b), because the potential is constant within the sphere, the electric potential at any radius r inside the charged shell is the same as on the surface of the sphere, V = kq/R. Using the given quantities, R = 2 m, and q = 61 µC, the potential is calculated using V = (8.99 × 10^9 N·m²/C²)(61 × 10^-6 C) / 2 m, which gives V = 272.5 volts.