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A 10 C charge is given to a conducting s...

A 10 C charge is given to a conducting spherical shell, and a-3 C point charge is placed inside the shell. For this arrangement, find the correct statement(s).

A

The charge on the inner surface of the shell will be `+3 C`, and it can be distributed uniformly or nonuniformly

B

The charge on the inner surface of the shell will be `+3 C`, and it can be distributed would be uniform.

C

The net charge on the outer surface of the shell will be` _7 C`, and its distribution can be uniform or nonuniform

D

The net charge on the outer surface of the shell will be `+7 C`, and its distribution would be uniform.

Text Solution

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The correct Answer is:
To solve the problem, we need to analyze the situation involving a conducting spherical shell with a charge distribution. Here’s a step-by-step breakdown of the solution: ### Step 1: Understand the Charge Distribution We have a conducting spherical shell that has a total charge of +10 C. Inside this shell, there is a point charge of -3 C. ### Step 2: Determine the Charge on the Inner Surface According to Gauss's law, the charge induced on the inner surface of a conductor is equal in magnitude and opposite in sign to the charge enclosed within it. Therefore, since there is a -3 C charge inside the shell, the inner surface of the shell will have a charge of +3 C. ### Step 3: Calculate the Charge on the Outer Surface The total charge on the shell is +10 C. Since the inner surface has +3 C, the charge on the outer surface can be calculated as follows: \[ \text{Charge on outer surface} = \text{Total charge} - \text{Charge on inner surface} = 10 C - 3 C = 7 C \] ### Step 4: Analyze the Distribution of Charges - The charge on the inner surface (+3 C) can be distributed either uniformly or non-uniformly depending on the position of the -3 C charge. If the -3 C charge is at the center, the distribution will be uniform; otherwise, it will be non-uniform. - The charge on the outer surface (+7 C) will always be uniformly distributed because it is a conductor and the charges will move to the outer surface and distribute evenly. ### Step 5: Evaluate the Statements 1. **Statement A**: The charge on the inner surface of the shell will be +3 C and can be distributed uniformly or non-uniformly. **(Correct)** 2. **Statement B**: The charge on the inner surface of the shell will be +3 C and will be distributed uniformly. **(Incorrect, as we cannot confirm uniform distribution without knowing the position of the -3 C charge)** 3. **Statement C**: The net charge on the outer surface of the shell will be -7 C and its distribution can be uniform or non-uniform. **(Incorrect, the charge is +7 C, not -7 C)** 4. **Statement D**: The net charge on the outer surface of the shell will be +7 C and its distribution will be uniform. **(Correct)** ### Final Conclusion The correct statements are A and D. ---
To solve the problem, we need to analyze the situation involving a conducting spherical shell with a charge distribution. Here’s a step-by-step breakdown of the solution: ### Step 1: Understand the Charge Distribution We have a conducting spherical shell that has a total charge of +10 C. Inside this shell, there is a point charge of -3 C. ### Step 2: Determine the Charge on the Inner Surface According to Gauss's law, the charge induced on the inner surface of a conductor is equal in magnitude and opposite in sign to the charge enclosed within it. Therefore, since there is a -3 C charge inside the shell, the inner surface of the shell will have a charge of +3 C. ...
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