Three charges, q1 = 1 µC, q2 = 2 µC and q3 = 3 µC are placed in a line with 20 cm between each of them. So qiat r = 0, 92 at x 20 cm and q3 at a = 40 cm. Calculate the energy stored in the collection of charges.
Three charges, q1 = 1 µC, q2 = 2 µC and q3 = 3 µC are placed in a line with 20 cm between each of them. So qiat r = 0, 92 at x 20 cm and q3 at a = 40 cm. Calculate the energy stored in the collection of charges.
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![### Problem Statement:
Three charges, \( q_1 = 1 \, \mu C \), \( q_2 = 2 \, \mu C \), and \( q_3 = 3 \, \mu C \), are placed in a line with a 20 cm separation between each of them. Therefore, \( q_1 \) is at \( x = 0 \), \( q_2 \) is at \( x = 20 \, cm \), and \( q_3 \) is at \( x = 40 \, cm \). Calculate the energy stored in the collection of charges.
#### Multiple Choices:
(a) \(-0.62 \, J\)
(b) \(-0.43 \, J\)
(c) \(+0.43 \, J\)
(d) \(+0.62 \, J\)
#### Explanation:
To solve this problem, one needs to calculate the potential energy stored in the system of charges. The potential energy \( U \) between two point charges \( q_i \) and \( q_j \) separated by a distance \( r \) is given by the formula:
\[ U_{ij} = \frac{k \cdot q_i \cdot q_j}{r} \]
where \( k \) is Coulomb's constant (\( 8.99 \times 10^9 \, N \, m^2/C^2 \)).
1. Calculate the potential energy between \( q_1 \) and \( q_2 \):
\[ U_{12} = \frac{k \cdot q_1 \cdot q_2}{r_{12}} \]
with \( r_{12} = 0.2 \, m \).
2. Calculate the potential energy between \( q_1 \) and \( q_3 \):
\[ U_{13} = \frac{k \cdot q_1 \cdot q_3}{r_{13}} \]
with \( r_{13} = 0.4 \, m \).
3. Calculate the potential energy between \( q_2 \) and \( q_3 \):
\[ U_{23} = \frac{k \cdot q_2 \cdot q_3}{r_{23}} \]
with \( r_{23} = 0.2 \, m \](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fabbe649f-9542-4750-a644-5a898c154717%2F621daf10-693f-485c-b3d3-08b2fc047b7e%2F0w8qdjl_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem Statement:
Three charges, \( q_1 = 1 \, \mu C \), \( q_2 = 2 \, \mu C \), and \( q_3 = 3 \, \mu C \), are placed in a line with a 20 cm separation between each of them. Therefore, \( q_1 \) is at \( x = 0 \), \( q_2 \) is at \( x = 20 \, cm \), and \( q_3 \) is at \( x = 40 \, cm \). Calculate the energy stored in the collection of charges.
#### Multiple Choices:
(a) \(-0.62 \, J\)
(b) \(-0.43 \, J\)
(c) \(+0.43 \, J\)
(d) \(+0.62 \, J\)
#### Explanation:
To solve this problem, one needs to calculate the potential energy stored in the system of charges. The potential energy \( U \) between two point charges \( q_i \) and \( q_j \) separated by a distance \( r \) is given by the formula:
\[ U_{ij} = \frac{k \cdot q_i \cdot q_j}{r} \]
where \( k \) is Coulomb's constant (\( 8.99 \times 10^9 \, N \, m^2/C^2 \)).
1. Calculate the potential energy between \( q_1 \) and \( q_2 \):
\[ U_{12} = \frac{k \cdot q_1 \cdot q_2}{r_{12}} \]
with \( r_{12} = 0.2 \, m \).
2. Calculate the potential energy between \( q_1 \) and \( q_3 \):
\[ U_{13} = \frac{k \cdot q_1 \cdot q_3}{r_{13}} \]
with \( r_{13} = 0.4 \, m \).
3. Calculate the potential energy between \( q_2 \) and \( q_3 \):
\[ U_{23} = \frac{k \cdot q_2 \cdot q_3}{r_{23}} \]
with \( r_{23} = 0.2 \, m \
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