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A magnet of magnetic dipole moment 5.0 A m² is lying in a uniform magnetic field of 7×10⁻⁴ T such that its dipole moment vector makes an angle of 30° with the field. The work done in increasing this angle from 30° to 45° is about ......... J.

Asked in RS Academy GUJCET booklet · Dipole in a uniform field

• (1) 5.56×10⁻⁴
• (2) 24.74×10⁻⁴
• (3) 30.3×10⁻⁴
• (4) 5.50×10⁻³

Step-by-step solution

Why the other options are wrong

• (2) 24.74×10⁻⁴ is mB cos 45° by itself - only the final term. Work is a change of energy, so both terms are needed: mB(cos 30°-cos 45°).
• (3) 30.3×10⁻⁴ is mB cos 30° by itself - only the initial term. Subtracting the final term leaves 5.56×10⁻⁴ J.
• (4) Adds the two cosines instead of subtracting them: mB(cos 30°+cos 45°)=5.50×10⁻³ J. The energy is -mB cos θ, so the work between two angles is a difference.

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