A solid silver sphere of radius a = 2.5 cm has a net charge Qin = - 3.0 mC. The sphere is surrounded by a concentric copper spherical shell of inner radius b = 6.0 cm and outer radius c = 9.0 cm. The shell has a net charge Qout = +2.0 mC. A) What is the electric potential at the outer edge of the copper shell, given the potential at infinity is zero? B) What is the electric potential on the inner edge of the copper shell? C) What is the electric potential at the center of the silver sphere?

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aristocles aristocles · Answer 1 · 2019-10-02T07:13:59+02:00

Answer:

Part a)

tex]V = -1 \times 10^8 Volts[/tex]

Part b)

[tex]V_{inner} = V_{outer} = -1 \times 10^8 volts[/tex]

Part c)

[tex]V = -7.30 \times 10^8 Volts[/tex]

Explanation:

Part a)

Net charge distribution on each shell is given as

On surface of radius "a"

[tex]q_a = -3.0 mC[/tex]

on radius "b"

[tex]q_b = 3 mC[/tex]

on radius "c"

[tex]q_c = -1.0 mC[/tex]

Now potential at the outer shell is

[tex]V = \frac{kq_c}{r_c}[/tex]

[tex]V = \frac{(9\times 10^9)((-1\times 10^{-3})}{0.09}[/tex]

[tex]V = -1 \times 10^8 Volts[/tex]

Part b)

Since copper sphere is a conducting sphere so here it will be an equi potential surface

So the potential will remain same throughout the surface of this sphere

Now we can say

[tex]V_{inner} = V_{outer} = -1 \times 10^8 volts[/tex]

Part c)

Now electric potential at inner sphere is given as

[tex]V = \frac{kq_a}{r_a} + \frac{kq_b}{r_b} + \frac{kq_c}{r_c}[/tex]

[tex]V = \frac{(9\times 10^9)(-3 mC)}{0.025} + \frac{(9\times 10^9)(3 mC)}{0.06} + \frac{(9\times 10^9)(-1 mC)}{0.09}[/tex]

[tex]V = -7.30 \times 10^8 Volts[/tex]