JAMB - Physics (2025 - No. 70)
At what distance from a 1.2 x 10\(^{-7}\)C point charge will the electric field intensity be equal to 4.8 x 10\(^{-4}\)NC\(^{-1}\) [ Take \(\frac{1}{4\pi ε_0}\) = 9.0 x 10\(^9\)]
1.5Km
3.0Km
2.0Km
4.5Km
Explanation
B. 3.0 km
Using the formula for the electric field due to a point charge:
\(E = \frac{1}{4 \pi \epsilon_0} \frac{q}{r^2}\)
Given: \(E = 4.8 \times 10^{-4} \, \text{N/C}, \quad q = 1.2 \times 10^{-7} \, \text{C}, \quad \frac{1}{4 \pi \epsilon_0} = 9.0 \times 10^9 \, \text{Nm}^2/\text{C}^2\)
Rearranging:
\(r^2 = \frac{(9.0 \times 10^9) \times (1.2 \times 10^{-7})}{4.8 \times 10^{-4}} = 9 \times 10^6\)
Thus, \(r = \sqrt{9 \times 10^6} = 3000 \, \text{m} = 3.0 \, \text{km}\)
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