1. tan²θ=tan²θ₁+tan²θ₂ 2. cot²θ=cot²θ₁-cot²θ₂ 3. tan²θ=tan²θ₁-tan²θ₂ 4. cot²θ=cot²θ₁+cot²θ₂

Answer: 4. cot²θ=cot²θ₁+cot²θ₂ Key idea: in a vertical plane at angle α to the magnetic meridian, tanθ'=tanθ/cosα , i.e. cotθ'=cotθcosα . For two perpendicular planes the angles are α and 90^°-α : cot²θ₁+cot²θ₂=cot²θ(cos²α+sin²α)=cot²θ .

Topic: Torque on magnetic dipole in uniform field· Magnetic Effects of Current and Magnetism

If θ_1 and θ_2 be the apparent angles of dip observed in two vertical planes at right angles to each other, then the true angle of dip θ is given by :

1. \(\tan^2\theta=\tan^2\theta_1+\tan^2\theta_2\)

2. \(\cot^2\theta=\cot^2\theta_1-\cot^2\theta_2\)

3. \(\tan^2\theta=\tan^2\theta_1-\tan^2\theta_2\)

4. \(\cot^2\theta=\cot^2\theta_1+\cot^2\theta_2\)

Doubtly Asked 30 Oct 2026 NEET UG 2017 neet Save WhatsApp Report

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Answer: 4. \(\cot^2\theta=\cot^2\theta_1+\cot^2\theta_2\)

Key idea: in a vertical plane at angle \(\alpha\) to the magnetic meridian, \(\tan\theta'=\dfrac{\tan\theta}{\cos\alpha}\), i.e. \(\cot\theta'=\cot\theta\cos\alpha\).

For two perpendicular planes the angles are \(\alpha\) and \(90^\circ-\alpha\):

\(\cot^2\theta_1+\cot^2\theta_2=\cot^2\theta(\cos^2\alpha+\sin^2\alpha)=\cot^2\theta\).

Doubtly AI · 30 Oct 2026 AI-generated · not yet verified Report

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If θ_1 and θ_2 be the apparent angles of dip observed in two vertical planes at right angles to each other, then the true angle of dip θ is given by :

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