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### Fundamentals Of Physics

Book edition 10th Edition
Author(s) David Halliday
Pages 1328 pages
ISBN 9781118230718

# Figure 21-20 shows three identical conducting bubbles A, B, and C floating in a conducting container that is grounded by a wire. The bubbles initially have the same charge. Bubble A bumps into the container’s ceiling and then into bubble B. Then bubble B bumps into bubble C, which then drifts to the container’s floor. When bubble C reaches the floor, a charge of is transferred upward through the wire, from the ground to the container, as indicated. (a) What was the initial charge of each bubble? When (b) bubble A and (c) bubble B reach the floor, what is the charge transfer through the wire? (d) During this whole process, what is the total charge transfer through the wire?

• a) The initial charge of each bubble is.
• b) When bubble A reaches the floor, the charge transfer through the wire is -2e.
• c) When bubble B reaches the floor, the charge transfer through the wire is- 3e.
• d) During this whole process, the total charge transfer through the wire is -12e.

See the step by step solution

## Stating given data

• a) Figure 21-20 shows three identical conducting bubbles A, B, and C floating in a conducting container that is grounded by a wire.
• b) The bubbles have the same charge.

c) When bubble C reaches the floor, the charge transfer upward through the wire is -3e

## Step 2: Understanding  concept of charging by conduction

When two charged bodies are brought in contact with each other, the total charge of the system is divided among the given charged bodies equally until they have the same charge as per their volume. This process is called charging by conduction. Thus, using this concept, the charges on each body can be calculated.

## Step 3: a) Calculation of initial charge of each bubble

Let the charge on each bubble initially be q.

At first, when bubble A comes in contact with the container surface, it becomes neutral with charge ${q}_{A}=0$.

Now, after it comes in contact with bubble B, their charges get equally distributed as per the concept. Thus, the new charge on A and B becomes

${q}_{A}\text{'}={q}_{B}\text{'}\phantom{\rule{0ex}{0ex}}=\frac{0+q}{2}\phantom{\rule{0ex}{0ex}}=\frac{q}{2}$

Now, after bubble B comes in contact with bubble C, their charges get equally distributed as per the concept. Thus, the new charge on B and C becomes

localid="1663082080063"

Thus, the final charges become ${q}_{A}\text{'}=q/2,{q}_{B}\text{'}\text{'}=3q/4,{q}_{C}\text{'}=3q/4$ .

So, as per the given data, the charge is being transferred through the wire in the upward direction for bubble C reaching the floor. Thus, as per the concept, any charge in contact with the ground becomes neutral and so the net charge on C should be zero after final transfer.

So, the final charge on C that is transferred by the bubble is equal to the negative value -3e for the transfer to happen. That implies

3q / 4= -(-3e) q=4e

Hence, the initial charge is 4e.

## Step 4: b) Calculation of charge transferred by A when it reaches floor

When A reaches the floor, it transfers all its charges to the ground, Thus, the net charge transferred is negative for the flow of charge through the wire to happen.

That implies

${q}_{A}\text{'}=-\left(q/2\right)\phantom{\rule{0ex}{0ex}}=-\left(4e/2\right)\phantom{\rule{0ex}{0ex}}=-2e$

Hence, the net charge transferred by A is -2e.

## Step 5: c) Calculation of charge transferred by B when it reaches floor

When B reaches the floor, it transfers all its charges to the ground. Thus, the net charge transferred is negative for the flow of charge through the wire to happen.

That implies

${q}_{B}\text{'}\text{'}=-\left(3q/4\right)\phantom{\rule{0ex}{0ex}}=-\left(3\left(4e\right)/4\right)\phantom{\rule{0ex}{0ex}}=-3e$

Hence, the net charge transferred by A is -3e .

## Step 6: d) Calculation of net charge transferred by all bubbles

The net charge transferred by all the bubbles during the whole process is given by

${q}^{\text{'}}=-\left(3q\right)\phantom{\rule{0ex}{0ex}}=-3\left(4e\right)\phantom{\rule{0ex}{0ex}}=-12e$

Hence, the total charge transferred is -12e .