Question

1. what will the charge be on each of the spheres after they have come in contact?

-6 0
-4 +2
-5 -9
+7 +3

Explanation:

To solve for the charge on each sphere after contact, we use the principle that when two conducting spheres come into contact, their total charge is shared equally between them. The formula for the final charge \( Q_{\text{final}} \) on each sphere is:

$$ Q_{\text{final}} = \frac{Q_1 + Q_2}{2} $$

First Pair: \(-6\) and \(0\)

Step 1: Sum the Charges

Total charge \( = -6 + 0 = -6 \)

Step 2: Divide by 2 (Equal Sharing)

Final charge \( = \frac{-6}{2} = -3 \)

Second Pair: \(-4\) and \(+2\)

Step 1: Sum the Charges

Total charge \( = -4 + 2 = -2 \)

Step 2: Divide by 2

Final charge \( = \frac{-2}{2} = -1 \)

Third Pair: \(-5\) and \(-9\)

Step 1: Sum the Charges

Total charge \( = -5 + (-9) = -14 \)

Step 2: Divide by 2

Final charge \( = \frac{-14}{2} = -7 \)

Fourth Pair: \(+7\) and \(+3\)

Step 1: Sum the Charges

Total charge \( = 7 + 3 = 10 \)

Step 2: Divide by 2

Final charge \( = \frac{10}{2} = 5 \)

Final Answers (per pair, top to bottom):

1. \(\boldsymbol{-3}\) (for \(-6\) and \(0\))
2. \(\boldsymbol{-1}\) (for \(-4\) and \(+2\))
3. \(\boldsymbol{-7}\) (for \(-5\) and \(-9\))
4. \(\boldsymbol{+5}\) (for \(+7\) and \(+3\))

Answer:

To solve for the charge on each sphere after contact, we use the principle that when two conducting spheres come into contact, their total charge is shared equally between them. The formula for the final charge \( Q_{\text{final}} \) on each sphere is:

$$ Q_{\text{final}} = \frac{Q_1 + Q_2}{2} $$

First Pair: \(-6\) and \(0\)

Step 1: Sum the Charges

Total charge \( = -6 + 0 = -6 \)

Step 2: Divide by 2 (Equal Sharing)

Final charge \( = \frac{-6}{2} = -3 \)

Second Pair: \(-4\) and \(+2\)

Step 1: Sum the Charges

Total charge \( = -4 + 2 = -2 \)

Step 2: Divide by 2

Final charge \( = \frac{-2}{2} = -1 \)

Third Pair: \(-5\) and \(-9\)

Step 1: Sum the Charges

Total charge \( = -5 + (-9) = -14 \)

Step 2: Divide by 2

Final charge \( = \frac{-14}{2} = -7 \)

Fourth Pair: \(+7\) and \(+3\)

Step 1: Sum the Charges

Total charge \( = 7 + 3 = 10 \)

Step 2: Divide by 2

Final charge \( = \frac{10}{2} = 5 \)

Final Answers (per pair, top to bottom):

1. \(\boldsymbol{-3}\) (for \(-6\) and \(0\))
2. \(\boldsymbol{-1}\) (for \(-4\) and \(+2\))
3. \(\boldsymbol{-7}\) (for \(-5\) and \(-9\))
4. \(\boldsymbol{+5}\) (for \(+7\) and \(+3\))