30. Induction and Inductance

CALC Let's look at the details of eddy-current braking. A square loop, length l on each side, is shot with velocity v₀ into a uniform magnetic field B. The field is perpendicular to the plane of the loop. The loop has mass m and resistance R, and it enters the field at t = 0 s. Assume that the loop is moving to the right along the x-axis and that the field begins at x = 0 m. Find an expression for the loop's velocity as a function of time as it enters the magnetic field. You can ignore gravity, and you can assume that the back edge of the loop has not entered the field.

The magnetic field B at all points within the colored circle shown in Fig. E29.15 has an initial magnitude of 0.750 T. (The circle could represent approximately the space inside a long, thin solenoid.) The magnetic field is directed into the plane of the diagram and is decreasing at the rate of -0.0350 T/s. What is the emf between points a and b on the ring?

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CALC An electric generator has an 18-cm-diameter, 120-turn coil that rotates at 60 Hz in a uniform magnetic field that is perpendicular to the rotation axis. What magnetic field strength is needed to generate a peak voltage of 170 V?

According to Faraday's Law, what physical quantity is induced in a closed loop by a changing magnetic field?

(II) The magnetic field perpendicular to a single 13.2-cm-diameter circular loop of copper wire decreases uniformly from 0.760 T to zero. If the wire is 2.25 mm in diameter, how much charge moves past a point in the coil during this operation?

The magnetic field within a long, straight solenoid with a circular cross section and radius R is increasing at a rate of dB/dt. What is the magnitude of the induced emf if the radius in part (d) is 2R?

According to $Faraday’s$ Law, if a magnetic field through a closed loop increases into the page, what is the direction of the induced current in the loop?

According to Faraday's Law, if the magnetic flux $\Phi$ through a conducting loop in figure 1 is increasing into the page, what is the direction of the induced current in the loop?

FIGURE EX30.13 shows a 10-cm-diameter loop in three different magnetic fields. The loop's resistance is 0.20 Ω. For each, what are the size and direction of the induced current?

According to Faraday's Law, the induced electromotive force ($\mathrm{emf}$) in a closed loop is equal to which of the following quantities?

(II) A simple generator has a 440-loop square coil 22.0 cm on a side. How fast must it turn in a 0.550-T field to produce a 120-V peak output?

According to $Faraday’sLaw$, is there an induced current in a $solenoid$ when $magnet1$ is moved away from it?

(II) A single circular loop of wire is placed inside a long solenoid with its plane perpendicular to the axis of the solenoid. The area of the loop is A₁ and that of the solenoid, which has n turns per unit length, is A₂. A current I = I₀ cos ωt flows in the solenoid turns. What is the induced emf in the small loop?

CALC A 5.0-cm-diameter coil has 20 turns and a resistance of 0.50 Ω. A magnetic field perpendicular to the coil is B = 0.020t + 0.010t², where B is in tesla and t is in seconds. Find an expression for the induced current I(t) as a function of time.

(III) Design a dc transmission line that can generate 625 MW of electricity and transmit it 485 km with only a 2.0% loss. The wires are to be made of aluminum and the voltage is 660 kV.