A closely wound solenoid of 2000 turns and area of cross-section 1.5 × 10-4 m 2 carries a current of 2.0 A. It is suspended through its center and perpendicular to its length, allowing it to turn in a horizontal plane in a uniform magnetic field 5 × 10-2 T, making an angle of 30° with the axis of the solenoid. The torque on the solenoid will be

Question

A closely wound solenoid of 2000 turns and area of cross-section 1.5 × 10-4 m 2 carries a current of 2.0 A. It is suspended through its center and perpendicular to its length, allowing it to turn in a horizontal plane in a uniform magnetic field 5 × 10-2 T, making an angle of 30° with the axis of the solenoid. The torque on the solenoid will be (A) 3 × 10-3 N - m (B) 1.5 × 10-3 N - m (C) 1.5 × 10-2 N - m (D) 3 × 10-2 N - m

Tardigrade Admin · Accepted Answer

τ =N i B A sin θ =2000 × 2 × 5 × 10-2 × 1.5 × 10-4 × sin 30° =2000 × 50 × 10-6 × (1/2) =1.5 × 10-2 N - m

$3 \times 1 0^{- 3} N - m$

$1.5 \times 1 0^{- 3} N - m$

$1.5 \times 1 0^{- 2} N - m$

$3 \times 1 0^{- 2} N - m$

$τ = N i B A sin θ$
$= 2000 \times 2 \times 5 \times 1 0^{- 2} \times 1.5 \times 1 0^{- 4} \times sin 3 0^{\circ}$
$= 2000 \times 50 \times 1 0^{- 6} \times \frac{1}{2}$
$= 1.5 \times 1 0^{- 2} N - m$

3×10−3N−m

1.5×10−3N−m

1.5×10−2N−m

3×10−2N−m

τ=NiBAsinθ =2000×2×5×10−2×1.5×10−4×sin30∘ =2000×50×10−6×21​ =1.5×10−2N−m

$3 \times 1 0^{- 3} N - m$

$1.5 \times 1 0^{- 3} N - m$

$1.5 \times 1 0^{- 2} N - m$

$3 \times 1 0^{- 2} N - m$

$τ = N i B A sin θ$
$= 2000 \times 2 \times 5 \times 1 0^{- 2} \times 1.5 \times 1 0^{- 4} \times sin 3 0^{\circ}$
$= 2000 \times 50 \times 1 0^{- 6} \times \frac{1}{2}$
$= 1.5 \times 1 0^{- 2} N - m$