Question

Three negatively charged spheres, each with a charge of 4.0 x 10 6 C, are fixed at the
vertices of an equilateral triangle whose sides are 20 cm long. Calculate the magnitude and
direction of the net electric force on each sphere.

Answer 1

Given info : Three negatively charged spheres, each with a charge 4 × 10¯⁶ C are fixed at the vertices of an equilateral triangle whose sides are 20cm long.

To find : the magnitude and direction of the net electric force on each sphere are...

solution : let ABC is an equilateral triangle and three given charge are placed at vertices A , B and C respectively.

let's find electric force exerted due to A and B on C.

electric force due to A on C , F₁ = Kq²/r²

electric force due to B on C, F₂ = kq²/r²

angle between them is 60° so net force , F = √{F₁² + F₂² + 2F₁F₂cos60°} = √3kq²/r²

now putting, q = 4 × 10¯⁶ C , r = 0.2 m

so, F = √3 × 9 × 10^9 × (4 × 10¯⁶)²/(0.2)²

= 1.732 × 9 × 10¯³ × 64/0.04

= 1.732 × 9 × 1.6

≈ 25 N

direction of force, tanΦ = sinθ/(1 + cosθ)

= sin60°/(1 + cos60°)

= (√3/2)/(3/2)

= 1/√3

= tan30°

so, Φ = 30°

Therefore angle made by resultant with each force is 30°

Answer 2

Answer:

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