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A spherical metal shell A of radius RA a...

A spherical metal shell A of radius `R_A` and a solid metal sphere B of radius `R_B(ltR_A)` are kept far apart and each is given charge `'+Q'`. Now they are connected by a thin metal wire. Then

A

(a) `E_A^`(inside)=`0`

B

(b) `Q_AgtQ_B`

C

(c) `(sigmaA)/(sigmaB)=(R_B)/(R_A)`

D

(d) `E_A^`(on surface)`ltE_B^`(on surface)

Text Solution

Verified by Experts

The correct Answer is:
A, B, C, D
Electric field inside a spherical metallic shell with charge on the surface is always zero. Therefore option [a] is correct. When the shells are connected with a thin metal wire then electric potentials will be equal, say V.
`:.` `(1)/(4pi in_0)(Q_A)/(R_A)=(1)/(4pi in_0)(Q_B)/(R_B)=V`
As `R_AgtR_B` therefore `Q_AgtA_B`. option [b] is also correct.
As `(sigmaA)/(sigmaB)=((Q_A)/(4piR_A^2))/((Q_B)/(4piR_B^2))=(R_B^2)/(R_A^2)xx(Q_A)/(Q_B)=(R_B^2)/(R_A^2)xx(4pi in_0R_AV)/(4pi in_0R_BV)`
`:.` `(sigma_A)/(sigma_B)=(R_B)/(R_A)` Option (c) is also correct
Also `E_A=(sigma_A)/(in_0)` & `E_B=(sigma_B)/(in_0)`
`E_A/E_B=(sigma_A)/(sigma_B)=R_B/R_Alt1` `:.` `E_AltE_B`
Option (d) is also correct
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