Given:
- Four point charges, each with a magnitude of 1.2 nC, are located at the corners of a square with a side length of 4 cm.
To find:
- The total potential energy stored in the system.
Solution:
The potential energy between two point charges can be calculated using the formula:
U = k*q1*q2/r
Where U is the potential energy, k is the Coulomb's constant, q1 and q2 are the magnitudes of the charges, and r is the distance between the charges.
Since we have four charges in this system, we need to calculate the potential energy between each pair of charges and then sum them up to find the total potential energy.
Calculating the potential energy between each pair of charges:
1. Potential energy between charges at opposite corners:
U1 = k*q1*q2/r
= (9 x 10^9 Nm^2/C^2)(1.2 x 10^-9 C)(1.2 x 10^-9 C)/(4 x 10^-2 m)
= 3.24 x 10^-3 J
2. Potential energy between charges at adjacent corners:
U2 = k*q1*q2/r
= (9 x 10^9 Nm^2/C^2)(1.2 x 10^-9 C)(1.2 x 10^-9 C)/(4 x 10^-2 m)
= 3.24 x 10^-3 J
3. Potential energy between charges at the same corner (self-energy):
U3 = k*q1*q2/r
= (9 x 10^9 Nm^2/C^2)(1.2 x 10^-9 C)(1.2 x 10^-9 C)/(0 m)
= Infinity (As the distance between the charges is zero, the potential energy becomes infinite)
Total potential energy:
The total potential energy is the sum of the potential energy between each pair of charges:
UTotal = U1 + U2 + U3
= (3.24 x 10^-3 J) + (3.24 x 10^-3 J) + ∞
= ∞ (As the self-energy is infinite, the total potential energy is also infinite)
Therefore, the given answer option 'A' (1.75 J) is incorrect. The correct answer is 'D' (0 J) as the total potential energy stored in the system is zero.