A bar magnet is hung by a thin cotton thread in a uniform horizontal magnetic field and is in equilibrium state. The energy required to rotate it by $60^{\circ}$ is $W$. Now the torque required to keep the magnet in this new position is
- $\frac{W}{\sqrt{3}}$
- $\sqrt{3} W$
- $\frac{\sqrt{3} W}{2}$
- $\frac{2W}{\sqrt{3}}$
The Correct Option is B
Solution and Explanation
Work and Torque Calculation
Let's start with the calculation of work (W) and torque (τ) for the given situation.
Work Calculation:
Work is calculated as:
\(W = MB \left(\cos 0^{\circ} - \cos 60^{\circ}\right)\)
Substituting the values for cosine:
\(W = MB \left(1 - \frac{1}{2}\right) = \frac{MB}{2}\)
Torque Calculation:
The required torque for this position is:
\(τ = MB \sin θ\)
Substituting the value for sine of 60°:
\(τ = MB \sin 60^{\circ} = \frac{\sqrt{3}}{2} MB = \sqrt{3} W\)
Conclusion:
Therefore, the required torque is \(τ = √3 W\).
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Concepts Used:
Magnetism & Matter
Magnets are used in many devices like electric bells, telephones, radio, loudspeakers, motors, fans, screwdrivers, lifting heavy iron loads, super-fast trains, especially in foreign countries, refrigerators, etc.
Magnetite is the world’s first magnet. This is also called a natural magnet. Though magnets occur naturally, we can also impart magnetic properties to a substance. It would be an artificial magnet in that case.
Read More: Magnetism and Matter
Some of the properties of the magnetic field lines are:
- The lines and continuous and outside the magnet, the field lines originate from the North pole and terminate at the South pole
- They form closed loops traversing inside the magnet.
- But here the lines seem to originate from the South pole and terminate at the North pole to form closed loops.
- More number of close lines indicate a stronger magnetic field
- The lines do not intersect each other
- The tangent drawn at the field line gives the direction of the field at that point.