The concentric, conducting spherical shells $X, Y$ and $Z$ with radii $r, 2 r$ and $3 r$ , respectively. $X$ and $Z$ are connected by a conducting wire and $Y$ is uniformly charged to charge $Q$ as shown in figure. Charges on shells $X$ and $Z$ will be

Question

The concentric, conducting spherical shells

X, Y

and

Z

with radii

r, 2 r

and

3 r

, respectively.

X

and

Z

are connected by a conducting wire and

Y

is uniformly charged to charge

Q

as shown in figure. Charges on shells

X

and

Z

will be

The concentric, conducting spherical shells X, Y and Z with radii r, 2 r and 3 r , respectively. X and Z are connected

Quantrex Academy · Accepted Answer

Correct answer: B. q_x=(-Q)/(4), q_z=(Q)/(4)

Let charges on X and Z be q_x and q_Z By conservation of charge, q_x+q_z=0 q_z=-q_x aligned V_x & =(1)/(4 π _0)[(q_x)/(r)+(Q)/(2 r)+(q_z)/(3 r)] V_z & =(1)/(4 π _0)[(q_x)/(3 r)+(Q)/(3 r)+(q_z)/(3 r)] aligned Since, X and Z are connected. V_x=V_Z aligned & & (q_X)/(r)+(Q)/(2 r)+(q_Z)/(3 r) & =(q_X)/(3 r)+(Q)/(3 r)+(q_Z)/(3 r) & & (2 q_X)/(3) & =(-Q)/(6) & & q_X & =(-Q)/(4) & & q_X+q_Z & =0 q_Z=-q_X & & & =(Q)/(4) aligned

The concentric, conducting spherical shells X, Y and Z with radii...

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