A solenoid of length 0.4 m and having 500 turns of wire carries a current of 3.0 A. A thin coil having 10 turns of wire and of radius 0.01 m carries a current of 0.4 A. Calculate the torque required to hold the coil in the middle of the solenoid with its axis perpendicular to the axis of the solenoid.

Question

A solenoid of length 0.4 m and having 500 turns of wire carries a current of 3.0 A. A thin coil having 10 turns of wire and of radius 0.01 m carries a current of 0.4 A. Calculate the torque required to hold the coil in the middle of the solenoid with its axis perpendicular to the axis of the solenoid. (A) 6×106 N (B) 5.94×10-6 Nm (C) 9.54×106 Nm (D) 5.9×10-8 Nm

Tardigrade Admin · Accepted Answer

Magnetic field at the middle of the solenoid, B =

m_{0} n I = m_{0} \frac{N}{L} I

=

4 π \times 1 0^{- 7} \times \frac{500}{0.4} \times 3 = 4.713 \times 1 0^{- 3}

T.
Magnetic dipole moment of the coil, M = NIA = NI

π r^{2}

=

10 \times 0.4 \times 3.142 \times (0.01)^{2} = 1.26 \times 1 0^{- 3} A m^{2}

Torque acting on the coil

τ

= MB sin

θ

=

1.26 \times 1 0^{- 3} \times 4.713 \times 1 0^{- 3} = 5.94 \times 1 0^{- 6}

Nm

$6 \times 1 0^{6} N$

$5.94 \times 1 0^{- 6} N m$

$9.54 \times 1 0^{6} N m$

$5.9 \times 1 0^{- 8} N m$

6×106N

5.94×10−6Nm

9.54×106Nm

5.9×10−8Nm

Magnetic field at the middle of the solenoid, B = m0​nI=m0​LN​I = 4π×10−7×0.4500​×3=4.713×10−3T. Magnetic dipole moment of the coil, M = NIA = NIπr2 = 10×0.4×3.142×(0.01)2=1.26×10−3Am2 Torque acting on the coil τ = MB sin θ = 1.26×10−3×4.713×10−3=5.94×10−6Nm

$6 \times 1 0^{6} N$

$5.94 \times 1 0^{- 6} N m$

$9.54 \times 1 0^{6} N m$

$5.9 \times 1 0^{- 8} N m$