Magnetic Field Produced by Loops and Solenoids Video Lessons

Concept

Problem: A 1200-turn coil of wire 2.10 cm in diameter in a magnetic field that increases from 0 T to 0.110 T in 11.0 ms. The axis of the coil is parallel to the field.What is the emf of the coil?Express your answer to two significant figures and include the appropriate units.

FREE Expert Solution

The induced emf in a coil of N turns is:

$\overline{){\mathbf{\epsilon }}{\mathbf{=}}{\mathbf{N}}{\mathbf{|}}\frac{\mathbf{d}{\mathbf{\varphi }}_{\mathbf{m}}}{\mathbf{d}\mathbf{t}}{\mathbf{|}}}$, where N is the number of turns, and ϕm is magnetic flux.

The magnetic flux ϕm is given by:

$\overline{)\begin{array}{rcl}{\mathbf{\varphi }}_{\mathbf{m}}& {\mathbf{=}}& \mathbf{B}\mathbf{·}\mathbf{A}\\ & {\mathbf{=}}& \mathbf{B}\mathbf{A}\mathbf{c}\mathbf{o}\mathbf{s}\mathbf{\theta }\end{array}}$

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Problem Details

A 1200-turn coil of wire 2.10 cm in diameter in a magnetic field that increases from 0 T to 0.110 T in 11.0 ms. The axis of the coil is parallel to the field.

What is the emf of the coil?
Express your answer to two significant figures and include the appropriate units.