Question

Four point charges are placed at the corners of a square ABCD of side 10 cm, as shown in figure.

The force on a charge of 1 $\mu C$placed at the centre of square is

• A. 7 N
• B. 8 N
• C. 2 N
• D. Zero

Answer 1

Answer: (D)

Zero

Answer 2

: From figure, length of diagonal of the square

$= AC = BD = \sqrt{10^{2} + 10^{2}} = 10\sqrt{2}cm$

$OA = OB = OC = OD = \frac{10\sqrt{2}}{2} = \frac{10}{\sqrt{2}}cm$

Forces of repulsion on $1\mu C$ charge at O due to $3\mu C$ charge, at A and C are equal and opposite. So they cancel each other. Similarly, forces of attraction of $1\mu C$ charge at O due to $- 4\mu C$ charges at B and D are also equal and opposite. So they also cancel each other.

Hence the net force on the charge of $1\mu C$ at O is zero.