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Problem 3: The L-shaped conductor in Fig. 3 moves at v = 10 m/s across and touches a stationary L-shaped conductor in a B = 0.1 T magnetic field. The two vertices overlap, so that the enclosed area is zero, at t = 0s. The conductor has a resistance of r = 0.01 ohms per meter. Find the induced emf and current at t = 0.1 s. a) Find the formula for the side of the loop, x, as a function of time. Note that the rate with which x is growing is equal not to the full speed of the conductor, v, but to the horizontal projection of its velocity. Assuming that the loop stays a square at all times, derive the formula for the magnetic flux through it as a function of t. ● ● ● ● ● X ● stationary ● c) Compute the numerical values of & and I at t = 0.1 s. (Partial answer: I = 35 A) B=QIT 45° 15-10 FIG. 3: The scheme for Problem 2 b) Derive the formula for the induced emf, & = |d, and the induced current I in the loop. Which formula do you need to use for the resistance of the loop?

Problem 3: The L-shaped conductor in Fig. 3 moves at v = 10 m/s across and touches a stationary L-shaped conductor in a B = 0.1 T magnetic field. The two vertices overlap, so that the enclosed area is zero, at t = 0s. The conductor has a resistance of r = 0.01 ohms per meter. Find the induced emf and current at t = 0.1 s. a) Find the formula for the side of the loop, x, as a function of time. Note that the rate with which x is growing is equal not to the full speed of the conductor, v, but to the horizontal projection of its velocity. Assuming that the loop stays a square at all times, derive the formula for the magnetic flux through it as a function of t. ● ● ● ● ● X ● stationary ● c) Compute the numerical values of & and I at t = 0.1 s. (Partial answer: I = 35 A) B=QIT 45° 15-10 FIG. 3: The scheme for Problem 2 b) Derive the formula for the induced emf, & = |d, and the induced current I in the loop. Which formula do you need to use for the resistance of the loop?

College Physics
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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Hello, I really need help with part A,part B and part C because I don't know why I keep getting the wrong answer and I tried everything is there any chance you can help me with Part A,Part B, and Part C and can you label them as well

**Problem 3:** The L-shaped conductor in Fig. 3 moves at \( v = 10 \, \text{m/s} \) across and touches a stationary L-shaped conductor in a \( B = 0.1 \, \text{T} \) magnetic field. The two vertices overlap, so that the enclosed area is zero, at \( t = 0 \, \text{s} \). The conductor has a resistance of \( r = 0.01 \, \text{ohms per meter} \). Find the induced emf and current at \( t = 0.1 \, \text{s}. a) Find the formula for the side of the loop, \( x \), as a function of time. Note that the rate with which \( x \) is growing is equal not to the full speed of the conductor, \( v \), but to the horizontal projection of its velocity. Assuming that the loop stays a square at all times, derive the formula for the magnetic flux through it as a function of \( t \). b) Derive the formula for the induced emf, \( \mathcal{E} = \left| \frac{d\Phi}{dt} \right| \), and the induced current \( I \) in the loop. Which formula do you need to use for the resistance of the loop? c) Compute the numerical values of \( \mathcal{E} \) and \( I \) at \( t = 0.1 \, \text{s} \). (Partial answer: \( I = 35 \, \text{A} \)) **Diagram Explanation:** - **Figure 3:** Illustrates the motion of the L-shaped conductor where one conductor is stationary, and the other is moving diagonally at an angle of \( 45^\circ \) with an initial velocity of \( v = 10 \, \text{m/s} \). - The area enclosed by the overlapping conductors changes as one conductor moves horizontally. - The magnetic field \( B = 0.1 \, \text{T} \) is uniform and perpendicular to the plane of the conductors, represented by dots in the diagram. The blue line indicates the stationary conductor and the orange line the moving conductor.
Transcribed Image Text:**Problem 3:** The L-shaped conductor in Fig. 3 moves at \( v = 10 \, \text{m/s} \) across and touches a stationary L-shaped conductor in a \( B = 0.1 \, \text{T} \) magnetic field. The two vertices overlap, so that the enclosed area is zero, at \( t = 0 \, \text{s} \). The conductor has a resistance of \( r = 0.01 \, \text{ohms per meter} \). Find the induced emf and current at \( t = 0.1 \, \text{s}. a) Find the formula for the side of the loop, \( x \), as a function of time. Note that the rate with which \( x \) is growing is equal not to the full speed of the conductor, \( v \), but to the horizontal projection of its velocity. Assuming that the loop stays a square at all times, derive the formula for the magnetic flux through it as a function of \( t \). b) Derive the formula for the induced emf, \( \mathcal{E} = \left| \frac{d\Phi}{dt} \right| \), and the induced current \( I \) in the loop. Which formula do you need to use for the resistance of the loop? c) Compute the numerical values of \( \mathcal{E} \) and \( I \) at \( t = 0.1 \, \text{s} \). (Partial answer: \( I = 35 \, \text{A} \)) **Diagram Explanation:** - **Figure 3:** Illustrates the motion of the L-shaped conductor where one conductor is stationary, and the other is moving diagonally at an angle of \( 45^\circ \) with an initial velocity of \( v = 10 \, \text{m/s} \). - The area enclosed by the overlapping conductors changes as one conductor moves horizontally. - The magnetic field \( B = 0.1 \, \text{T} \) is uniform and perpendicular to the plane of the conductors, represented by dots in the diagram. The blue line indicates the stationary conductor and the orange line the moving conductor.
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