JEE MAIN - Physics (2025 - 23rd January Evening Shift - No. 14)
Explanation
$$ U = \frac{1}{4\pi\epsilon_0} \frac{q_1 q_2}{r} $$
Here,
$$ q_1 = 7 \times 10^{-6} \, C $$
$$ q_2 = -4 \times 10^{-6} \, C $$
The separation between the charges is along the x-axis from $$ -7 \, \text{cm} $$ to $$ 7 \, \text{cm} $$, so
$$ r = 0.14 \, m $$
The Coulomb constant is approximated as
$$ \frac{1}{4\pi\epsilon_0} \approx 9 \times 10^9 \, \frac{Nm^2}{C^2} $$
Substitute these values into the equation:
$$ U = 9 \times 10^9 \times \frac{(7 \times 10^{-6})(-4 \times 10^{-6})}{0.14} $$
Calculate the product of the charges:
$$ (7 \times 10^{-6})(-4 \times 10^{-6}) = -28 \times 10^{-12} \, C^2 $$
Now, divide by the distance:
$$ \frac{-28 \times 10^{-12}}{0.14} = -2 \times 10^{-10} \, C^2/m $$
Finally, multiply by the Coulomb constant:
$$ U = 9 \times 10^9 \times (-2 \times 10^{-10}) = -1.8 \, J $$
Thus, the electrostatic potential energy of the configuration is:
$$ -1.8 \, J $$
This corresponds to Option D.
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