Back(II) The area of an elastic circular loop decreases at a constant rate, dA/dt = -3.50 x 10-2 m2/s. The loop is in a magnetic field B = 0.35 T whose direction is perpendicular to the plane of the loop. At t = 0, the loop has area A = 0.285 m2. Determine the induced emf at t = 0, and at t = 2.00 s.
(II) A circular wire loop of radius 𝓇 = 12 cm is in a uniform magnetic field B = 0.400 T with its plane perpendicular to the direction of the field. If the field magnitude begins to decrease at a rate of -0.010 T/s, at what rate should 𝓇 be increasing at this instant so that the induced emf within the loop is zero?
A circular loop in the plane of the paper lies in a 0.65-T uniform magnetic field pointing into the paper. The loop’s diameter changes from 20.0 cm to 8.0 cm in 0.50 s. What is (a) the direction of the induced current, (b) the magnitude of the average induced emf, and (c) the average induced current if the coil resistance is 2.5Ω?
(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?
(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?
A circular loop of area 12 m² encloses a magnetic field perpendicular to the plane of the loop; its magnitude is B(t) = (8.0 T/s)t. The loop is connected to a 7.5-Ω resistor and a 6.5-pF capacitor in series. When fully charged, how much charge is stored on the capacitor?
What is the energy dissipated as a function of time in a circular loop of 18 turns of wire having a radius of 10.0 cm and a resistance of 2.0 Ω if the plane of the loop is perpendicular to a magnetic field given by B(t) = B₀e⁻ᵗ/ʳ with B₀ = 0.50 T and τ = 0.10 s?
Magnetic flux passes through a stationary loop of wire with resistance R and this flux varies from t = 0, to t = T/2 such that Φ(t) = b sin(2𝝅t/T) where b is a given constant. Estimate the energy dissipated in the loop during that time.
(III) In a circular region, there is a uniform magnetic field pointing into the page (Fig. 29–56). An xy coordinate system has its origin at the circular region’s center. A free positive point charge +Q = 1.0 μC is initially at rest at a position x = +10 cm on the x axis. If the magnitude of the magnetic field is now decreased at a rate of -0.10 T/s, what force (magnitude and direction) will act on +Q?
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?
(III) Determine the emf induced in the square loop in Fig. 29–52 if the loop stays at rest and the current in the straight wire is given by I(t) = (15.0 A) sin (2200 t) where t is in seconds. The distance a is 12.0 cm, and b is 15.0 cm.
(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?
(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.
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 current in the ring if its resistance is 4.00 Ω?
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