A flat coil having 160 turns,each with an area of 0.20 m²,is placed with the plane of its area perpendicular to a 0.40T $\vec { B }$ field.The magnitude of the $\vec { B }$ field changes uniformly from 0.40 T in the +x direction to 0.40 T in the -x direction in 2.0 s.If the resistance of the coil is 16 Ω,at what rate is power generated in the coil during this change? A)5.0 W B)10 W C)15 W D)20 W

Question

Quizplus · Accepted Answer

The power generated in the coil can be calculated using Faraday's Law of electromagnetic induction and the power formula. Faraday's Law states that the induced electromotive force (EMF) in a coil is equal to the negative rate of change of magnetic flux through the coil. The power generated (P) is then given by $P = \frac{E^2}{R}$, where $E$ is the induced EMF and $R$ is the resistance.Given:- Number of turns ($N$) = 160- Area of each turn ($A$) = 0.20 m$^2$- Change in magnetic field ($\Delta B$) = 0.80 T (from +0.40 T to -0.40 T, so the total change is 0.80 T)- Time interval ($\Delta t$) = 2.0 s- Resistance ($R$) = 16 $\Omega$The change in magnetic flux ($\Delta \Phi$) is given by $\Delta \Phi = N \cdot A \cdot \Delta B$.The induced EMF ($E$) can be calculated using Faraday's Law: $E = -\frac{\Delta \Phi}{\Delta t}$.Substituting the given values:$\Delta \Phi = 160 \times 0.20 \times 0.80 = 25.6$ Wb$E = -\frac{25.6}{2.0} = -12.8$ V (The negative sign indicates the direction of the EMF, which is not needed for power calculation.)The power generated is:$P = \frac{E^2}{R} = \frac{12.8^2}{16} = \frac{163.84}{16} = 10.24$ W, which rounds to 10 W, considering significant figures and the context of the question.

A Flat Coil Having 160 Turns,each with an Area of 0.20