Question

three concentric conducting spherical shells have radii a, b, c such that x< b (a) Find the electric potential of the three shells.
(b) If the inner and outer shells are now connected by a wire that is insulated as it passes through the middle shell, what is the electric potential of each of the three shells, and what is the final charge on each shell?

Answer 1

Answer:

a) $V_{A} =\frac{KQ(c-b)}{bc}$

$V_{B} =\frac{KQ(c-b)}{bc}$

Vc = 0

b) qA = 0

qB = Q

qC = -Q

VA = VC = 0

$V_{B} =\frac{KQ(c-b)}{bc}$

Explanation:

a) The electric potential of the three shells are:

$V_{A} =\frac{KQ}{b} +\frac{K(-Q)}{c} =KQ(\frac{1}{b} -\frac{1}{c} )=\frac{KQ(c-b)}{bc}$

$V_{B} =\frac{KQ}{b} +\frac{K(-Q)}{c} =KQ(\frac{1}{b} -\frac{1}{c} )=\frac{KQ(c-b)}{bc}$

$V_{c} =\frac{KQ}{c} +\frac{K(-Q)}{c} =0$

b) When the inner shell is connected with another, both will have the same potential, then:

qA = 0

qB = Q

qC = -Q

$V_{a} =V_{c}\frac{KQ}{c} +\frac{K(-Q)}{c} =0$

$V_{B} =\frac{KQ}{b} +\frac{K(-Q)}{c} =KQ(\frac{1}{b} -\frac{1}{c} )=\frac{KQ(c-b)}{bc}$