### Magnetic Field and Induced Current in a Coil**Problem Statement:**The area of a 200-turn coil is \(0.02 \, \text{m}^2\). The resistance of the coil is \(64 \, \Omega\). If the coil is oriented with its surface perpendicular to a magnetic field \(B\), at what rate in \(\text{T/s}\) should the magnitude of \(B\) change to induce a current of \(0.25 \, \text{A}\) in the coil?1. \( \bigcirc \) 320 \(\text{T/s}\)2. \( \bigcirc \) 800 \(\text{T/s}\)3. \( \bigcirc \) 4 \(\text{T/s}\)4. \( \bigcirc \) 2 \(\text{T/s}\)5. \( \bigcirc \) 0.5 \(\text{T/s}\)**Explanation:**This problem involves calculating the rate of change of the magnetic field (in Tesla per second, \(\text{T/s}\)) required to induce a specific current in the coil.To solve the problem, we use Faraday's Law of Induction and Ohm's Law:1. **Faraday's Law of Induction**: \[ \mathcal{E} = -N \frac{d\Phi_B}{dt} \] Where: - \(\mathcal{E}\) is the induced EMF (in volts, \(V\)). - \(N\) is the number of turns in the coil. - \(\frac{d\Phi_B}{dt}\) is the rate of change of magnetic flux.2. **Magnetic Flux (\(\Phi_B\))**: \[ \Phi_B = B \cdot A \] Where: - \(B\) is the magnetic field (in teslas, \(T\)). - \(A\) is the area of the coil (in square meters, \(\text{m}^2\)).3. **Ohm’s Law**: \[ I = \frac{\mathcal{E}}{R} \] Where: - \(I\) is the current (in amperes, \(A\)). - \(R\) is the

Solution: Given: n = number of turns of wire in coil = 200 A = area of coil = 0.02 m2 R = resistance…

The area of a 200 turn coil is 0.02 m². The resistance of the coil is 64 02. If the coil is oriented with its surface perpendicular to a magnetic field B, at what rate in T/s should the magnitude of B change to induce a current of 0.25 A in the coil? 320 T/s 800 T/s 4 T/s 2 T/s 0.5 T/s

The area of a 200 turn coil is 0.02 m². The resistance of the coil is 64 02. If the coil is oriented with its surface perpendicular to a magnetic field B, at what rate in T/s should the magnitude of B change to induce a current of 0.25 A in the coil? 320 T/s 800 T/s 4 T/s 2 T/s 0.5 T/s

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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