Question

Four identical point charges of magnitude q = 3.2 nC are placed at the corners of a rhombus of edge length l = 22 cm and obtuse angle θ. We intentionally leave θ undefined. Find the net electric force on each of the four charges. Your answer will depend on the angleθ. For convenience, orient your rhombus so that the charges are placed at (±x, 0) and (0, ±y).

Answer 1

Figure shows the charges 3.2 nC placed at the corners of rhombus ABCD of side 22 cm. Let the origin of coordinate system be at centre of rhombus.

Let F_D be the resultant force on charge D due to other charges, which is given as

where K = coulomb's constant = 1/ () = 9 10⁹ Nm²C^-2 and angle is given by

First term of expression for F_A is due to the x-axis components of force due to charge at B and charge at D,

where as y-axis components of force due to charge at B and charge at D cancel each other.

Second term of expression for F_A is force due to the charge at C

we get F_A as , F_A = - 0.19 10^-5 { 2 sin (/2) + 0.25 cosec² (/2) } N

By symmetry F_C = -F_A

Let F_D be the resultant force on charge D due to other charges, which is given as

we get F_D as , F_D = - 0.19 10^-5 { 2 cos (/2) + 0.25 sec² (/2) } N

By symmetry F_B = - F_D