Physics Q36 – JEE-MAIN 2025

Home Physics Magnetism and MatterQuestion #245

A magnetic dipole experiences a torque of

80 \sqrt{3}

N m when placed in uniform magnetic field in such a way that dipole moment makes angle of

60^{\circ}

with magnetic field. The potential energy of the dipole is :

Clue 1 of 3: Fundamental Concepts

Recall the formulas for torque and potential energy of a magnetic dipole in a uniform magnetic field.

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Ninja Strategy•Sign Analysis

Recognize that for an angle between $0^{\circ}$ and $90^{\circ}$ , the potential energy of a magnetic dipole in a uniform field is always negative, eliminating positive options.

🧠 Full Solution Path

Step 1: Determine the product of magnetic moment and magnetic field (MB)✦ Active

The torque experienced by a magnetic dipole in a uniform magnetic field is given by the formula $τ = M B \sin θ$ . We are given $τ = 80 \sqrt{3}$ N m and $θ = 60^{\circ}$ . We can use this to find the product $M B$ .

τ = M B \sin θ 80 \sqrt{3} = M B \sin (60^{\circ}) 80 \sqrt{3} = M B (\frac{\sqrt{3}}{2}) M B = \frac{80 \sqrt{3} \times 2}{\sqrt{3}} M B = 160 J/T

Step 2: Calculate the potential energy of the dipole○ Expand

The potential energy of a magnetic dipole in a uniform magnetic field is given by the formula $U = - M B \cos θ$ . Now substitute the calculated value of $M B$ and the given angle $θ$ .

U = - M B \cos θ U = - 160 \cos (60^{\circ}) U = - 160 (\frac{1}{2}) U = - 80 J

💡 Teacher's Secret Hint

Remember that the potential energy is negative when the dipole moment is aligned with the field (or has a component along the field direction).

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Physics Question 36 – JEE-MAIN 2025

Clue 1 of 3: Fundamental Concepts

🧠 Full Solution Path