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The electrostatic potential on the surfa...

The electrostatic potential on the surface of a charged concducting sphere is `100 V`. Two statements are made in this regard
`S_(1) :` at any inside the sphere, electric intensity is zero.
`S_(2) :` at any point inside the sphere, the electrostatic potential is `100 V`.

A

`S_(1)` is true but `S_(2)` is false

B

Both `S_(1) and S_(2)` are false

C

`S_(1)` is true, `S_(2)`is also true and `S_(1)` is the cause of `S_(2)`

D

`S_(1)` is true, `S_(2)` is also true but the statements are independent.

Text Solution

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The correct Answer is:
To solve the problem, we need to analyze the two statements regarding the electrostatic potential and electric field inside a charged conducting sphere. ### Step-by-Step Solution: 1. **Understanding the Properties of Conductors:** - In electrostatics, when a conductor is charged, the electric field inside the conductor is zero. This is due to the movement of free electrons within the conductor, which redistribute themselves to cancel any internal electric fields. 2. **Electric Field Inside the Sphere:** - Since the electric field intensity (E) inside the conducting sphere is zero, we can state: \[ E = 0 \] - The relationship between electric field and potential is given by: \[ E = -\frac{dV}{dr} \] - If \(E = 0\), it implies that: \[ \frac{dV}{dr} = 0 \] - This means that the potential \(V\) is constant throughout the interior of the sphere. 3. **Potential Inside the Sphere:** - The problem states that the electrostatic potential on the surface of the charged conducting sphere is \(100 \, V\). Since the potential is constant inside the conductor, we conclude that: \[ V = 100 \, V \quad \text{(inside the sphere)} \] 4. **Evaluating the Statements:** - **Statement S1:** "At any point inside the sphere, electric intensity is zero." - This statement is **true** because we established that the electric field inside a charged conductor is zero. - **Statement S2:** "At any point inside the sphere, the electrostatic potential is \(100 \, V\)." - This statement is also **true** because the potential is constant and equal to the surface potential of \(100 \, V\). 5. **Conclusion:** - Both statements are true. However, the reason for the second statement being true is the first statement. Thus, we conclude: - S1 is true. - S2 is true. - S1 is the cause of S2. ### Final Answer: Both statements are true, and S1 is the reason for S2. ---
To solve the problem, we need to analyze the two statements regarding the electrostatic potential and electric field inside a charged conducting sphere. ### Step-by-Step Solution: 1. **Understanding the Properties of Conductors:** - In electrostatics, when a conductor is charged, the electric field inside the conductor is zero. This is due to the movement of free electrons within the conductor, which redistribute themselves to cancel any internal electric fields. 2. **Electric Field Inside the Sphere:** ...
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