Question:

Two charges +7 mC and -4 mC at coordinates (-7, 0, 0) and (7, 0, 0), respectively, find the electrostatic potential energy. ϵ0=8.85×1012C2N1m2. \epsilon_0 = 8.85 \times 10^{-12} \, \text{C}^2 \, \text{N}^{-1} \, \text{m}^{-2}.

Updated On: Jan 24, 2025
Hide Solution
collegedunia
Verified By Collegedunia

Solution and Explanation

The electrostatic potential energy U U between two point charges is given by the formula: U=kq1q2r, U = \frac{k q_1 q_2}{r}, where: - k=14πϵ0 k = \frac{1}{4 \pi \epsilon_0} is Coulomb’s constant, - q1=7mC=7×103C q_1 = 7 \, \text{mC} = 7 \times 10^{-3} \, \text{C} , - q2=4mC=4×103C q_2 = -4 \, \text{mC} = -4 \times 10^{-3} \, \text{C} , - r r is the distance between the charges. We can calculate the distance r r between the charges using the distance formula: r=(7(7))2+(00)2+(00)2=(14)2=14m. r = \sqrt{(7 - (-7))^2 + (0 - 0)^2 + (0 - 0)^2} = \sqrt{(14)^2} = 14 \, \text{m}. Now, using the value of Coulomb's constant k=14πϵ0 k = \frac{1}{4 \pi \epsilon_0} : k=14π×8.85×1012=9×109Nm2/C2. k = \frac{1}{4 \pi \times 8.85 \times 10^{-12}} = 9 \times 10^9 \, \text{N} \cdot \text{m}^2/\text{C}^2. Substitute the values into the formula for potential energy: U=9×109×(7×103)×(4×103)14. U = \frac{9 \times 10^9 \times (7 \times 10^{-3}) \times (-4 \times 10^{-3})}{14}. U=9×109×(28×106)14=18J. U = \frac{9 \times 10^9 \times (-28 \times 10^{-6})}{14} = -18 \, \text{J}. Thus, the electrostatic potential energy is 18J -18 \, \text{J} .
Was this answer helpful?
1
0