Question

if the balls touch each other at the same time and then separate, what’s the net charge on each ball now?
a one object has a net charge of -3 while the others -1
b they all have no charge
c each object has a net charge of + 2
d one object has a net charge of + 7 while the others 0
e each object has a net charge of + 1

Explanation:

Step1: Calculate total charge

First, find the sum of the charges: \( +7 + (-3) + (-1) = 7 - 3 - 1 = 3 \)? Wait, no, wait: \( +7 + (-3) + (-1) = 7 - 3 - 1 = 3 \)? Wait, no, 7 - 3 is 4, 4 - 1 is 3? Wait, no, the number of balls is 3? Wait, the three balls have charges +7, -3, -1. So total charge is \( 7 + (-3) + (-1) = 7 - 3 - 1 = 3 \)? Wait, no, 7 - 3 is 4, 4 -1 is 3? Wait, no, 7 + (-3) is 4, 4 + (-1) is 3. Then, when they touch, the charge redistributes equally among the three balls. Wait, no, wait: the total charge is \( 7 + (-3) + (-1) = 3 \)? Wait, no, 7 - 3 is 4, 4 -1 is 3. Then, each ball gets total charge divided by number of balls (3). So \( 3 \div 3 = 1 \)? Wait, no, wait: 7 + (-3) is 4, 4 + (-1) is 3? Wait, no, 7 - 3 -1 = 3? Wait, no, 7 -3 is 4, 4 -1 is 3. Then 3 divided by 3 is 1. Wait, but let's recalculate: +7 (first ball), -3 (second), -1 (third). Total charge: \( 7 + (-3) + (-1) = 7 - 3 - 1 = 3 \). Number of balls: 3. So each ball's charge is \( \frac{7 + (-3) + (-1)}{3} = \frac{3}{3} = 1 \)? Wait, no, 7 -3 is 4, 4 -1 is 3. 3 divided by 3 is 1. So each ball has +1? Wait, but let's check again. Wait, maybe I made a mistake. Wait, +7, -3, -1. Sum: 7 -3 =4, 4 -1=3. 3 divided by 3 is 1. So each ball has +1. So the correct option is e? Wait, option e is "Each object has a net charge of + 1". So that's the answer.

Wait, let's do it step by step:

Step1: Find total charge

The charges are \( q_1 = +7 \), \( q_2 = -3 \), \( q_3 = -1 \). Total charge \( Q = q_1 + q_2 + q_3 = 7 + (-3) + (-1) = 3 \).

Step2: Redistribute charge equally

When conductors (the balls, assuming they are conductors) touch, charge redistributes equally. There are 3 balls, so each ball gets \( \frac{Q}{3} = \frac{3}{3} = 1 \). So each ball has a net charge of +1.

Answer:

e. Each object has a net charge of + 1