A block of insulating material has a positive charge +Q_0 distributed uniformly
ID: 1524351 • Letter: A
Question
A block of insulating material has a positive charge +Q_0 distributed uniformly throughout its volume. The block is then broken into two pieces. A and B. as shown. A student makes the following statement: The charge density is calculated by dividing the total charge by the volume. Since the volume is in the denominator, a large volume will give a small charge density. Therefore, the block with the smallest volume, block B. will have the largest charge density. What, if anything, is wrong with this statement? If something is wrong, explain the error and how to correct It. If the statement is valid, explain why.Explanation / Answer
Charge density is the ratio of the charge and the volume containing it. It is given that initially, the charge was uniformly distributed over the block.
When the block is broken into pieces, the volume of the individual pieces is lesser than the total volume of the initial block but the total charge of the block also gets divided in a similar way. Therefore, as the denominator (which is the volume) decreases as we break the block, the numerator (charge) also decreases such that the ratio (charge density) remains constant.
Hence the given statement by the student is incorrect.
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