An ac generator consisting of a coil with $N$ turns rotating at angular speed $\omega$ in an external magnetic field $B$ produces a maximum emf $\varepsilon _ { 0 }$. If you now decrease the number of turns in the coil to $N / 2$ and at the same time cause it to rotate twice as fast, what will be the new maximum emf if you do not change any of the other quantities?
A) $4 \varepsilon _ { 0 }$
B) $\varepsilon _ { 0 } / 4$
C) $\varepsilon _ { 0 }$
D) $2 \varepsilon _ { 0 }$
E) $\varepsilon _ { 0 } / 2$

Question

Quizplus · Accepted Answer

The maximum emf ($\varepsilon_0$) generated by an AC generator is given by the formula $\varepsilon_0 = NAB\omega$, where $N$ is the number of turns, $A$ is the area of the coil, $B$ is the magnetic field strength, and $\omega$ is the angular velocity. If $N$ is halved and $\omega$ is doubled, the product $N\omega$ remains constant, meaning the maximum emf ($\varepsilon_0$) does not change.

An Ac Generator Consisting of a Coil With NNN Turns Rotating at Angular Speed

An Ac Generator Consisting of a Coil With $N$ Turns Rotating at Angular Speed