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• Notes

$\begin{array}{l}{\text { A single loop of wire with an area of } 0.0900 \mathrm{m}^{2} \text { is in a uni- }} \\ {\text { form magnetic field that has an initial value of } 3.80 \mathrm{T}, \text { is perpendi- }} \\ {\text { cular to the plane of the loop, and is decreasing at a constant rate of }} \\ {0.190 \mathrm{T} / \mathrm{s} \text { . ( a) What emf is induced in this loop? (b) If the loop has }} \\ {\text { a resistance of } 0.600 \Omega, \text { find the current induced in the loop. }}\end{array}$

$|\varepsilon|=\left|\frac{d \Phi_{B}}{d t}\right|$

$\Phi_{B}=BA cos \phi$

(a) $|\varepsilon|=A \frac{d B}{d t}=(0.09)(0.19)=0.0171 V$

(b) $\varepsilon=I R \rightarrow I=\frac{\varepsilon}{R}$

$=\frac{0.0171}{0.6}=0.0285 \mathrm{A}$

$\begin{array}{l}{\text { A circular loop of wire with a radius of } 12.0 \mathrm{cm} \text { and ori- }} \\ {\text { ented in the horizontal } x y-\text { plane is located in a region of uniform }} \\ {\text { magnetic field. A field of } 1.5 \mathrm{T} \text { is directed along the positive }} \\ {z \text { -direction, which is upward. (a) If the loop is removed from the }} \\ {\text { field region in a time interval of } 2.0 \mathrm{ms} \text { , find the average emf that }} \\ {\text { will be induced in the wire loop during the extraction process. }} \\ {\text { (b) If the coil is viewed looking down on it from above, is the }} \\ {\text { induced current in the loop clockwise or counterclockwise? }}\end{array}$

$\varepsilon=-\frac{\Delta \Phi_{B}}{\Delta t}$$=-\frac{\Phi_{\mathrm f}-\Phi_{i}}{\Delta t}$

$=-\frac{0-(1.5) \pi(0.12)^{2}}{2 * 10^{-3} \mathrm{5}}=+34 \mathrm{V}$

current is counterclockwise