At each corner of a square of side ℓ t..

Question

At each corner of a square of side ℓ there are positive point charges of magnitudes Q1=Q, Q2=8Q, Q3=9Q and Q4=6Q.

a.) Determine the magnitude of the force on the charge Q2.

b.) Determine the angle made by the direction of the net force acting on the charge Q2 with respect to the positive x-axis.

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Answer 1

Hello Emalia;

Q1 and Q3 are at a distance ℓ to Q2 whereas Q4 is ℓ√2 far.

All are positive, all push Q2 away.

F₍₁₂₎ {Force of Q1 on Q2} = k8Q²/ℓ² to the right (î) Let's temporarily name it 8F

F₍₃₂₎ {Force of Q3 on Q2} = k 72Q²/ℓ² to upward (j) Let's temporarily name it 72F

F₍₄₂₎ {Force of Q3 on Q2} = k48Q²/(ℓ√2)² = k24Q²/ℓ^2. Let's temporarily name it 24F = (F_(42)x12√2 right and F_(42)y12√2 up) To add up components, I resolved this diagonal force into its x and y components.

Total X-dimension net force = 8F + 12√2F = F(8 + 12√2) (î)

Total Y-dimension net force = 72F + 12√2F = F(72 + 12√2) (j)

Using Pythagorean theorem;

F(net) =∼ 92.4F = 92.4kQ²/ℓ²

b) We need to find arc tan((72 + 12√2) / (8 + 12√2)) =≅74.3°

I hope this helps Emalia, numbers were not super friendly....