Condering the situation of the previous question, two experiments wer conducted whose details are as given `:`
Experiment 1 `: Q = 10 mu C`
`q = 50 mu C`
`R = 15 cm`
`r =10 cm`
Experiment 2 `: Q = 20 mu C`
`q = 60 mu C`
`R = 15 cm `
` r= 10 cm `
In which case the potential difference between the shells is more ?

Options

A. Experiment 1
B. Experiment 2
C. Potential difference is equal in both the cases
D. Zero

Answer

To determine in which experiment the potential difference between the shells is greater, we will calculate the potential difference for both experiments step by step.

### Step 1: Understand the Formula for Potential Difference
The potential difference \( V \) between two spherical shells can be calculated using the formula:
\[ V = V_{\text{outer}} - V_{\text{inner}} = \frac{kQ}{R} - \frac{kq}{r} \]
where:
- \( k \) is Coulomb's constant (\( 9 \times 10^9 \, \text{N m}^2/\text{C}^2 \))
- \( Q \) is the charge on the outer shell
- \( q \) is the charge on the inner shell
- \( R \) is the radius of the outer shell
- \( r \) is the radius of the inner shell

### Step 2: Calculate Potential Difference for Experiment 1
Given:
- \( Q = 10 \, \mu C = 10 \times 10^{-6} \, C \)
- \( q = 50 \, \mu C = 50 \times 10^{-6} \, C \)
- \( R = 15 \, cm = 0.15 \, m \)
- \( r = 10 \, cm = 0.10 \, m \)

Calculate \( V_1 \):
\[ V_1 = \frac{kQ}{R} - \frac{kq}{r} \]
Substituting the values:
\[ V_1 = \frac{(9 \times 10^9)(10 \times 10^{-6})}{0.15} - \frac{(9 \times 10^9)(50 \times 10^{-6})}{0.10} \]
Calculating each term:
\[ V_1 = \frac{90 \times 10^3}{0.15} - \frac{450 \times 10^3}{0.10} \]
\[ V_1 = 600000 - 4500000 = -3900000 \, V \]

### Step 3: Calculate Potential Difference for Experiment 2
Given:
- \( Q = 20 \, \mu C = 20 \times 10^{-6} \, C \)
- \( q = 60 \, \mu C = 60 \times 10^{-6} \, C \)
- \( R = 15 \, cm = 0.15 \, m \)
- \( r = 10 \, cm = 0.10 \, m \)

Calculate \( V_2 \):
\[ V_2 = \frac{kQ}{R} - \frac{kq}{r} \]
Substituting the values:
\[ V_2 = \frac{(9 \times 10^9)(20 \times 10^{-6})}{0.15} - \frac{(9 \times 10^9)(60 \times 10^{-6})}{0.10} \]
Calculating each term:
\[ V_2 = \frac{180 \times 10^3}{0.15} - \frac{540 \times 10^3}{0.10} \]
\[ V_2 = 1200000 - 5400000 = -4200000 \, V \]

### Step 4: Compare the Potential Differences
Now we have:
- \( V_1 = -3900000 \, V \)
- \( V_2 = -4200000 \, V \)

To find out which potential difference is greater, we compare the absolute values:
\[ |V_1| = 3900000 \, V \quad \text{and} \quad |V_2| = 4200000 \, V \]

Since \( |V_2| > |V_1| \), we conclude that:
\[ \text{The potential difference in Experiment 2 is greater.} \]

### Final Answer
The potential difference between the shells is greater in Experiment 2.

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