Three point charges q, 2q and 8q are to be placed on a
. 9cm long straight line. Find the
. positions where the charges shouldbe placed such that the potential energy
. of this sysrem is minimum. In this situation, what is the
. electric field at the charge q due to the other two charges?

Explanation

To solve the problem of placing the charges \( q \), \( 2q \), and \( 8q \) on a 9 cm long straight line such that the potential energy of the system is minimized, we can follow these steps:

### Step 1: Understand the Arrangement of Charges
To minimize the potential energy, we should place the charges such that the larger charges are farther apart from each other. Thus, we can place charge \( q \) in between \( 2q \) and \( 8q \).

### Step 2: Assign Positions
Let’s denote the position of charge \( q \) as \( x \) cm from one end of the line. Therefore, the positions of the other charges will be:
- Charge \( 2q \) at position \( 0 \) cm.
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