Question

4. Three point-like charges are placed at the corners of a square, 34.0 cm on each side. Find the magnitude of the total electric field at the empty corner. Let q11 = 13.0 µC, q22 = 42.0 µC, q33 = 50.0 µC.
N/C

92 93 9i

Answer 1

Let the fourth vertex be q4.

According to Coulumb's Law, Electric Field due to a point-like charge, q at a distance r is given by:

E = kq/r² , where k = Coulumb's Constant = 9*10^9 Nm²/C²

Electric field due to q₁ , E₁ = kq₁/r², where q₁ = 13 μC and r = 34cm = 0.34 m( Along -ve xaxis)

Electric field due to q₂, E₂ = kq₂/r², where q₂ = 13 μC and r = 34 * √2 cm = 48.08cm = 0.48m ( at 45 degrees between -ve X-axis and +ve Y-Axis)

Electric field due to q₃, E₃ = kq₃/r², where q₃ = 13 μC and r = 34cm = 0.34 m ( Along +ve Y-Axis)

Magnitude of the Net Electric Field at q₄ = √(( E₁+ E₂Cos 45)² + (E₃+ E₂Sin 45)² )