# Electromotive force (EMF) induced in a rectangular loop

## Homework Statement:

A rectangular single loop of wire of length 0.035m and width 0.015m is positioned at 45° to a uniform magnetic field of 2.3T. The loop is rotated through 45° so that its plane is parallel to the magnetic field. Determine the electromotive force (e.m.f.) induced in the loop if the rotation takes 0.5s

## Relevant Equations:

emf = BAN cosθ

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## Answers and Replies

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Hi, so you have calculated the flux $\Phi_B = \int \vec B \cdot d\vec A$, but what is the relationship between Emf induced and the flux? Have you heard of Faraday's Law, which states that the emf induced is given by $Emf_{induced} = -N\frac{d\Phi_{B}}{dt}$. If you are assuming that this rotates at a constant speed, then you can change the formula to $Emf_{induced} = -N\frac{\Delta \Phi}{\Delta t}$.

Hope that is some help. I can answer more questions, but I am trying not to give the answer away.

Hello, thank you for your message! After some thought and looking around in textbooks etc. I believe that by using $Emf_{induced} = -N\frac{\Delta \Phi}{\Delta t}$ I have calculated the Emf to be $-1\frac{0 - (8.54\text{ x }10^{-4})}{0.5} = 1.708 \text{ x } 10^{-3} \text{ V}$

I hope this is correct?
Thank you