# Average induced emf in coil with turns

## Homework Statement

A closely wound rectangular coil of 95.0 turns has dimensions of 29.0 cm by 40.0 cm. The plane of the coil is rotated from a position where it makes an angle of 39.0 degrees with a magnetic field of 1.60 T to a position perpendicular to the field. The rotation takes 0.120 s.
What is the average emf induced in the coil?

## The Attempt at a Solution

ε=ΔB/Δt*(A*cos 39°)
ε=1.6/.120*(.116*cos39)
=1.20

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## Homework Statement

A closely wound rectangular coil of 95.0 turns has dimensions of 29.0 cm by 40.0 cm. The plane of the coil is rotated from a position where it makes an angle of 39.0 degrees with a magnetic field of 1.60 T to a position perpendicular to the field. The rotation takes 0.120 s.
What is the average emf induced in the coil?

## The Attempt at a Solution

ε=ΔB/Δt*(A*cos 39°)
ε=1.6/.120*(.116*cos39)
=1.20
Welcome to PF, susan14! Which formula do you have for the emf?

I have:
$$\mathcal{E}=-N {d\Phi \over dt}$$
where either ##\Phi = B_{\textit{perpendicular to A}} A## or ##\Phi = B A_{\textit{perpendicular to B}}##.

The average ##\mathcal{E}## would be:
$$\mathcal{E}_{average}=-N {\Delta\Phi \over \Delta t}=-N {\Phi_t - \Phi_0 \over t - 0}$$
where ##\Phi_0## is the magnetic flux at time t=0, and ##\Phi_t## is the magnetic flux at the final time t.

What would you get for ##\Phi_0## and for ##\Phi_t##?
And what did you do with the factor N?