Question

charges 5uC , -2uC ,3uC and -9uC are placed at the corners A,B,C and D of a square ABCD of side 1m . the noe electric potential at the centre of the square is A) -27 KV B) -27ROOT2 KV C) -90 KV D) ZERO

Answer 1

The charges 5uC, -2uC, 3uC and -9uC are placed at the corners A,B,C and D of a square ABCD of side 1m. The electric potential at the centre of the square is A) -27 kV B) -27√2 kV C) -90 kV D) zero

Solution.

Figure 1

We denote: $q_{1} = 5\mu C, q_{2} = -2\mu C, q_{3} = 3\mu C, q_{4} = -9\mu C, a = 1\mathrm{m}, r$ is half the length of the diagonal of the square, $P$ is the center of the square. According to the Pythagorarean theorem we find $r$ :

$$2 r = \sqrt {a ^ {2} + a ^ {2}} = a \sqrt {2}; r = \frac {a}{\sqrt {2}}.$$

Find the electric potential at the center of the square $(\varphi_P)$ :

$$\varphi_ {P} = \frac {k q _ {1}}{r} + \frac {k q _ {2}}{r} + \frac {k q _ {3}}{r} + \frac {k q _ {4}}{r} = \frac {k \sqrt {2} (q _ {1} + q _ {2} + q _ {3} + q _ {4})}{a} = - 2 7 \sqrt {2} \mathrm {k V},$$

where $k = 9 \cdot 10^{9} \frac{\mathrm{N} \cdot \mathrm{m}^{2}}{\mathrm{C}^{2}}$ is Coulomb's constant.

Answer: B.