An insulated conductor initiallly free from charge is charged by repeated contacts with a plate which after each contact is replenished to a charge `Q`. If `q` is the charge on the conductor after first operation prove that the maximum charge which can be given to the conductor in this way is `(Qq)/(Q-q)`
Text Solution
AI Generated Solution
To solve the problem, we need to analyze the charging process of the insulated conductor when it comes into contact with a charged plate. Let's break down the steps:
### Step 1: Initial Setup
Let the insulated conductor have a capacitance \( C_1 \) and the plate have a capacitance \( C_2 \). Initially, the conductor is uncharged.
### Step 2: First Contact
When the charged plate, which has a charge \( Q \), comes into contact with the insulated conductor, a charge \( q \) is transferred to the conductor. After the first operation, the charge on the conductor is \( q \).
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