Question

Note: Students must show all the work to get full creait. No formula sheet is needed. Each question is 20 points Four point charges “q” are located at the corner of a square of side “a" meter. All charges are negative except the one located at the origin. Find: (a) the magnitude and (b) the direction of the net force on the positive charge. 1)

Answer 1

Electric field due to the charge 1
E₁ = Kq/ r²
where r is the distance between the charge 1 and the origin.
hence
E₁ = kq /a²
Similarly E₃   = Kq/a²
And the E₂ = Kq / r²
for charge 2,  
r = 2^1/2a therefore
E₂ = Kq/ 2a²
Now We take the component of E₂ along Y and Z axis
E_2y = E₂Cos45
E_2z = E₂Sin45
Hence the Net electric field in the Z direction
E_z = E₁ + E₂Sin45 = Kq/a² + (Kq/ 2a²)Sin45
= 1.353[Kq/a²] -------------(1)
Similarly in the y direction
E_Y = E₂Cos45 + E₃
= 1.353[Kq/a²] -------(2)
Hence the magnitude of the Electric field
E = (E_z² + E_y²)^1/2 = 1.914[Kq/a²]
Hence the magnitude of the force = qE
= 1.914[Kq² /a²]
And the direction of the force would be same as that of field
$\theta$ = tan^-1(E_Z /E_Y) = 45
Hence the direction of the force would be 45 from the Y axis in the anticlockwise direction.