A square loop PQRS having 10 turns, area 3.6 × 10⁻³ m² and resistance 100 Ω is slowly and uniformly being pulled out of a uniform magnetic field of magnitude B = 0.5 T as shown. Work done in pulling the loop out of the field in 1.0 s i $s _________$ × 10⁻⁶ J.

Question

G1 Physics · Accepted Answer

Image Let side of square loop be ℓ. Area: A = ℓ² = 3.6 × 10⁻³ m² The loop is pulled completely out in time t = 1 s. Therefore: v = ℓ/t Induced emf: ε = NBℓv Current: I = ε/R Magnetic retarding force: F = NIBℓ = N²B²ℓ²v/R Work done: W = Fℓ = N²B²ℓ³v/R Using: v = ℓ/t we get: W = N²B²ℓ⁴/(Rt) = N²B²A²/(Rt) Substituting: N = 10 B = 0.5 T A = 3.6 × 10⁻³ m² R = 100 Ω t = 1 s W = 3.24 × 10⁻⁶ J The source answer is entered as 3 after integer rounding.

A square loop PQRS having 10 turns, area 3.6 × 10⁻³ m² and resistance 100 Ω is slowly and uniformly being pulled out of a uniform magnetic field of magnitude B = 0.5 T as shown. Work done in pulling the loop out of the field in 1.0 s i s _________ × 10⁻⁶ J.