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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 = 0 s. 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, u, 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. ● ● ● ● ● ● ● ● ● c) Compute the numerical values of & and I at t = 0.1 s. (Partial answer: I = 35 A) ● stationary ↓ ● ● ● ● ● ● ● B=QIT ● 45° 15=10 m FIG. 3: The scheme for Problem 2 b) Derive the formula for the induced emf, E = |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 = 0 s. 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, u, 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. ● ● ● ● ● ● ● ● ● c) Compute the numerical values of & and I at t = 0.1 s. (Partial answer: I = 35 A) ● stationary ↓ ● ● ● ● ● ● ● B=QIT ● 45° 15=10 m FIG. 3: The scheme for Problem 2 b) Derive the formula for the induced emf, E = |d, and the induced current I in the loop. Which formula do you need to use for the resistance of the loop?

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Hi I really need help with part A, Part B and Part  C because I am having trouble with these three parts , I keep getting the wrong answer. Can you please help me with these three parts 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: \( I = 35 \, \text{A} \)) **Graph Explanation:** The diagram in Fig. 3 shows the L-shaped conductors: one stationary and the other moving at a 45-degree angle with velocity components. The magnetic field \( B = 0.1 \, \text{T} \) is represented by blue dots. The moving conductor has an indicated velocity vector composed of both horizontal and vertical components. The horizontal velocity component is \( 10\cos(45^\circ) \), and the vertical component is \( 10\sin(45^\circ) \). This setup is used to calculate the change in the area of the loop, affecting the magnetic flux over time, and consequently resulting in an induced emf and current as per Faraday's Law.
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: \( I = 35 \, \text{A} \)) **Graph Explanation:** The diagram in Fig. 3 shows the L-shaped conductors: one stationary and the other moving at a 45-degree angle with velocity components. The magnetic field \( B = 0.1 \, \text{T} \) is represented by blue dots. The moving conductor has an indicated velocity vector composed of both horizontal and vertical components. The horizontal velocity component is \( 10\cos(45^\circ) \), and the vertical component is \( 10\sin(45^\circ) \). This setup is used to calculate the change in the area of the loop, affecting the magnetic flux over time, and consequently resulting in an induced emf and current as per Faraday's Law.
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