A loop of wire is rotating around its vertical axis at an angular speed ω in a uniform magnetic field that is directed out of the page. Derive an equation for the induced Electromotive force (emf) as a function of time.
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A loop of wire is rotating around its vertical axis at an angular speed ω in a uniform magnetic field that is directed out of the page. Derive an equation for the induced Electromotive force (emf) as a function of time.
Introduction:
Faraday’s law of induction is a basic law of electromagnetism that predicts how a magnetic field will interact with an electric circuit to produce an electromotive force.
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- A single loop of copper wire, lying flat in a plane, has an area of 7.80 cm2 and a resistance of 1.50 Ω. A uniform magnetic field points perpendicular to the plane of the loop. The field initially has a magnitude of 0.500 T, and the magnitude increases linearly to 2.00 T in a time of 1.10 s. What is the induced current (in mA) in the loop of wire over this time?A square loop of dimensions 5.0 cm x 5.0 cm is initially in a 0.80-Tesla magnetic field, with its plane perpendicular to B; but it is removed from the field in 100 ms. What is the magnitude of emf induced in the loop?A conducting rod moves with a constant velocity in a direction perpendicular to a long, straight wire carrying a current I as shown in Figure. Find the magnitude of the emf generated between the ends of the rod.
- The loop in the figure has a resistance of 2.5 2 and is being pulled to the right at 1.0 m/s. X X X||X × X 2.0 T X||X 1.0 T 2.0 m X X X ||× × X X X X X • 2.0 m 2.0 m (a) Find the total magnetic flux through the loop, directed into the page, at the time instant shown. b)In the above problem, find the total magnetic flux through the loop, directed into the page, 2.0 s later. (c) In the above problem, find the magnitude of the induced current in the loop during this 2.0 s interval.A loop of wire sits in a uniform magnetic field, everywhere pointing toward you. Due to a changing magnetic flux through the loop, an induced current flows in the wire, clockwise as shown. The area of the loop is 0.610 m^2 , and the magnetic field initially has magnitude 0.950 T. Suppose that, over a time period of 2.23 s, the magnetic field changes from its initial value, producing an average induced voltage of 0.104 V. What is the final value of the magnetic field after this time period? 596 T 330 T 665 T 0.798 TConsider a straight conductor of length 9.7 cm. The conductor moves at right angles to a magnetic field of uniform strength B = 10-3 T generating e.m.f. of 2.5 × 10-³ V. Calculate the velocity of the straight conductor. Give your answer in SI units. Answer: Choose... +
- An electrically conductive rod is moving through a uniform magnetic flux at a constant velocity at right angles, as shown by its cross-section in the diagram. The velocity is in the x-direction, the rod is of length 150 mm along z, and the magnetic flux density is 0.2 T in the positive y-direction. Speed If the potential difference (voltage) across the ends of the rod is 5.8 Volts, what is the magnitude of the velocity? m/s Not perpendicular If the rod is passing through the flux with its axis not at right angles what can you be sure of? The speed to generate 5.8 V would have to be smaller. • The speed to generate 5.8 V would have to be bigger. The speed to generate 5.8 V would be the same.A power line carries a current I = 100 sin(380t), where I is in amps and t is in seconds. A clever engineering student wants to steal power by inducing emf in a rectangular loop of copper wire as shown below. If the student wants to induce a maximum emf in the loop equal to 1.7 V, what should be the length L of the loop? Assume that the magnetic field produced by the power line is uniform inside of the rectangular loo and equal to the magnetic field at the center of the loop. 5 mi To equipment I 0.5 mA loop of wire sits in a uniform magnetic field, everywhere pointing toward you. Due to a changing magnetic flux through the loop, an induced current flows in the wire, clockwise as shown. The area of the loop is 0.300 m^2 , and the magnetic field initially has magnitude 0.300 T. Suppose that, over a time period of 2.30 s, the magnetic field changes from its initial value, producing an average induced voltage of 0.020 V. What is the final value of the magnetic field after this time period?
- A conducting rod slides over two horizontal metal bars with a constant speed v to the left. The entire set up is in a region of uniform magnetic field that is perpendicular to the plane of the rod and bars. If the induced current through the resistor is as indicated, what is the direction of the magnetic field? R M out of the page into the page I V*Consider A rod of length 40 cm moving with a velocity of 30 m/s to the left in a magnetic field of 0.2 T into the page. The loop has a small resistance of 2 ohms. Find a) the emf in the loop b) the magnitude and direction of induced current c) the magnetic force acting on the rod and its direction