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A metallic spherical shell of radius r1 ...

A metallic spherical shell of radius `r_1` is surrounded by another concentric metallic spherical shell of radius `r_2`. The space between the two shells is filled with a dielectric of dielectric constant K. If a charge Q is given to the inner shell, the charge appearing on the outer surface of the outer shell is

A

`+Q`

B

`(+Qr_1^2)/r_2^2`

C

`(+QKr_1^2)/r_2^2`

D

`Q[1-1/K]`

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we need to analyze the situation with the two concentric metallic spherical shells and the charge distribution that occurs when a charge \( Q \) is placed on the inner shell. ### Step-by-Step Solution: 1. **Understanding the Setup**: We have two concentric metallic spherical shells: an inner shell with radius \( r_1 \) and an outer shell with radius \( r_2 \). The space between these shells is filled with a dielectric material of dielectric constant \( K \). 2. **Charge on the Inner Shell**: A charge \( Q \) is placed on the outer surface of the inner shell (radius \( r_1 \)). 3. **Induction of Charge**: The presence of charge \( Q \) on the inner shell will induce a charge on the inner surface of the outer shell (which is at radius \( r_2 \)). According to electrostatic principles, the inner surface of the outer shell will acquire a charge of \( -Q \) due to the electric field created by the charge \( Q \) on the inner shell. 4. **Charge Conservation**: Since the outer shell is metallic, it can redistribute its charges freely. The total charge on the outer shell must remain conserved. The outer surface of the outer shell will respond to the induced charge on its inner surface. 5. **Charge on the Outer Surface**: If the inner surface of the outer shell has a charge of \( -Q \), then to maintain the overall neutrality of the outer shell, the outer surface of the outer shell must have a charge of \( +Q \). This is because the outer shell itself is neutral, and the charges must balance out. 6. **Final Answer**: Therefore, the charge appearing on the outer surface of the outer shell is \( +Q \). ### Conclusion: The charge on the outer surface of the outer shell is \( +Q \). ---
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