Q146 / 160 · AP EAMCET 2022 (05 Jul Shift 2) · Physics
Electric potential due to a space is given by $\phi(x, y, z)=\phi_0 \frac{x_0}{x}$; when $x_0=5 \mathrm{~m}$ and $\phi_0=8 V$. Find the electric field at $(10 \mathrm{~m}, 5 \mathrm{~m}, 5 \mathrm{~m})$
- Correct answerA$0.40 \mathrm{Vm}^{-1} \hat{\mathrm{i}}$
- B$-0.40 \mathrm{Vm}^{-1} \hat{\mathrm{i}}$
- C$4.0 \mathrm{Vm}^{-1} \hat{\mathrm{i}}$
- D$-4.0 \mathrm{Vm}^{-1} \hat{\mathrm{i}}$
Solution
We have
$E=-\frac{d v}{d x}=-\frac{d}{d x} \frac{\left[\phi_0 x_0\right]}{x}=-\phi_0 x_0 \times-\frac{1}{x^2}=\frac{40}{x^2}$
So, $\left.\mathrm{E}\right|_{(10,5,5)}=\frac{40}{10^2}=0.4 \mathrm{~V} / \mathrm{m}$
Hence, the correct answer is option: 'A'.