Question

A closed Loop PQRS carrying a current is placed in a uniform magnetic field. If the magnetic forces on segment PS, SR and RQ are F₁, F₂ and F₃ respectively and are in the plane of the paper and along the directions shown, the force on the segment QP is _____________

(a) √[(F₃ – F₁)² – F₂²] 

(b) F₁ – F₂ + F₃

(c) – F₁ + F₂ + F₃

(d) √[(F₃ – F₁)² + F₂²]

Answer 1

The correct option (d) √[(F₃ – F₁)² + F₂²]

Explanation:

Let force F₄ is acting on segment QP.

From the figure

F₄cosθ = F₃ – F₁

F₄ sinθ = F₂

As F₄ = F₄(sin²θ + cos²θ)……….sin²θ + cos²θ = 1

∴ F₄ = F₄ [(F₂ / F₄)² + {(F₃ – F₁)/F₄}²]

F₄² = [F₂² + (F₃ – F₁)²]

F₄ = √[F₂² + (F₃ – F₁)²]