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 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.
Updated On: Jul 6, 2022
- $6\times10^6\,N$
- $5.94\times10^{-6}\,Nm$
- $9.54\times10^{6}\,Nm$
- $5.9\times10^{-8}\,Nm$
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The Correct Option is B
Solution and Explanation
Magnetic field at the middle of the solenoid, B = $m_0 nI = m_0 \frac{N}{L} I$
= $4 \pi \times 10^{-7} \times \frac{500}{0.4} \times 3 = 4.713 \times 10^{-3}$T.
Magnetic dipole moment of the coil, M = NIA = NI$\pi r^2$
= $10 \times 0.4 \times 3.142 \times (0.01)^2 = 1.26 \times 10^{-3} \, Am^2$
Torque acting on the coil $\tau $ = MB sin $\theta$
= $1.26 \times 10^{-3} \times 4.713 \times 10^{-3} = 5.94 \times 10^{-6} $Nm
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Concepts Used:
Torque
Torque is a moment of force. Torque is measured as a force that causeque is also defined as the turning effect of force on the axis of rotation. Torque is chs an object to rotate about an axis and is responsible for the angular acceleration. Characterized with “T”.
How is Torque Calculated?
Torque is calculated as the magnitude of the torque vector T for a torque produced by a given force F
T = F. Sin (θ)
Where,
r - length of the moment arm,
θ - the angle between the force vector and the moment arm.
Read More: Torque
Types of Torque
Torque is of two types:
- Static torque
- Dynamic torque