## Related questions with answers

A generator connected to the wheel or hub of a bicycle can be used to power lights or small electronic devices. A typical bicycle generator supplies 6.00 V when the wheels rotate at $\omega=20.0$ rad/s. If the generator's magnetic field has magnitude B = 0.600 T with N = 100 turns, find the loop area A.

Solution

VerifiedThe maximum emf induced in the coil is

$\varepsilon_{max}=N B A \omega$

We can express $A$ from above expression of maximum induced emf as

$\begin{equation}A=\dfrac{\varepsilon}{NB\omega} \end{equation}$

where, $\varepsilon_{max}=6\ \text{V}$ is the emf, $B=0.600\ \text{T}$ is the magnetic field, $N=100\ \text{turns}$ is the nnumber of turns, $\omega=20\ \frac{\text{rad}}{\text{s}}$ is the angular velocity.

Computing the above value in equation (1), we get

$\begin{align*} A & = \dfrac{\varepsilon_{max}}{NB\omega}\\ & = \dfrac{6\ \text{V}}{(100\ \text{turns})(0.600\ \text{T})(20\ \frac{\text{rad}}{\text{s}})}\\ & = 0.005\ \text{m}^2 \end{align*}$

Therefore, the area of the loop is $\boxed{A=0.005\ \text{m}^2}$

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