This is just like the gravity problems in Module 11. The electrical force depends directly on the charge involved. Whatever you multiply or divide the charge by, the force must be multiplied or divided by the same number. The force is also inversely related to the square of the distance. If you multiply the distance by 4, you must divide the force by 4 squared, or 16.

So…let’s look at this problem. First, we halve the charge of one object. That means we multiply the charge by 1/2. Thus, we must also multiply the force by 1/2. The second charge is reduced by a factor of 4, which means it is multiplied by 1/4. Thus, we multiply the force by 1/4 as well. In the end, then, the change in charges resulted in the force being multiplied by 1/2 and then again by 1/4, for a total of 1/8.

Now let’s look at distance. Remember, whatever we do to distance, we do the OPPOSITE to the force, and we also square it. The distance goes from 16 cm to 4 cm. What did we do to the distance? We DIVIDED by 4. If we DIVIDED the distance by 4, we MULTIPLY the force by 4 squared, which is 16.

So…what happened? The force got multiplied by 1/8 when we played with the charge, and it got multiplied by 16 when we played with the distance. Thus, the overall effect is to multiply by 1/2 and then multiply by 1/4, and then multiply by 16, which is the same as multiplying by 2. The new force, then, is 2 times the old force.