Faraday's law gives e = -dΦ/dt. For Φ = 3 sin t + 5 cos t, dΦ/dt = 3 cos t - 5 sin t, so e = -3 cos t + 5 sin t.
Formula / Key Relation
e = -dΦ/dt
Φ = 3sin t + 5cos t
dΦ/dt = 3cos t - 5sin t
e = -3cos t + 5sin t
Detailed Explanation
Concept & ReasoningThe induced emf polarity is governed by Lenz's law, represented by the minus sign in Faraday's law. Differentiate each term of flux with respect to time, then apply the negative sign to the entire derivative. The derivative of sin t is cos t and of cos t is -sin t. Thus dΦ/dt = 3cos t - 5sin t and e = -3cos t + 5sin t.How to Solve It in the ExamDifferentiate first, apply Lenz's minus sign last.Important Exam PointKeep track of both the derivative sign of cos t and Faraday's leading minus sign.Related Revision PathThis question sits…
Concept & Reasoning
The induced emf polarity is governed by Lenz's law, represented by the minus sign in Faraday's law. Differentiate each term of flux with respect to time, then apply the negative sign to the entire derivative. The derivative of sin t is cos t and of cos t is -sin t. Thus dΦ/dt = 3cos t - 5sin t and e = -3cos t + 5sin t.
How to Solve It in the Exam
Differentiate first, apply Lenz's minus sign last.
Important Exam Point
Keep track of both the derivative sign of cos t and Faraday's leading minus sign.
Related Revision Path
This question sits in the revision path Electromagnetic Fields → Electromagnetic Induction → Faraday's Law .
Quick Trick
Differentiate first, apply Lenz's minus sign last.
Common Mistake
Applying the minus sign to only one term is a common algebra error.
Exam Tip
Keep track of both the derivative sign of cos t and Faraday's leading minus sign.
SEO + Knowledge GraphRelated PYQs & Exam ContextExam path, knowledge path and deeper practice links.
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