The ring is rotated about a diameter with a constant angular velocity ω. At time t = 0 the plane of the ring is perpendicular to the magnetic field; the direction of the magnetic field does not change in time. (a) Obtain an expression for the induced emf as a function of time. (b) If ω = 400 rad/s, a = 20.0 cm, R = 0.0500 Ω, B0 = 0.150 T, and τ = 0.0300 s, what is the induced current I at t = 0? Answers:
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The ring is rotated about a diameter
with a constant
plane of the ring is perpendicular to the magnetic field;
the direction of the magnetic field does not change in
time. (a) Obtain an expression for the induced emf as a
function of time. (b) If ω = 400 rad/s, a = 20.0 cm, R =
0.0500 Ω, B0 = 0.150 T, and τ = 0.0300 s, what is the
induced current I at t = 0?
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- Suppose the base unit of an inductive charger produces a 1.10×10^-3 T magnetic field. Varying this magnetic field magnitude changes the flux through a 16.0 turn circular loop in the device, creating an emf that charges its battery. Suppose the loop area is 3.25×10^-4 m^2 and the induced emf has an average magnitude of 5.50V. Calculate the time required (in s) for the magnetic field to decrease to zero from its max valueAn elastic circular conductor expands at a constant rate with time so that its radius is given by r (t) = r_0 + vt, where r_0 = 0.1m and v = 0.015m / s. The loop has a constant resistance of R = 12Ω and is placed in a uniform magnetic field of magnitude B_0 = 0.75T, perpendicular to its plane, as shown in the figure. Find the direction and magnitude of the induced current, i_ {ind}, at t = 5s.A 44.0 mA current is carried by a uniformly wound air-core solenoid with 480 turns, a 11.0 mm diameter, and 10.0 cm length. (a) Compute the magnetic field inside the solenoid. HT (b) Compute the magnetic flux through each turn. T-m2 (c) Compute the inductance of the solenoid. mH (d) Which of these quantities depends on the current? (Select all that apply.) O magnetic field inside the solenoid magnetic flux through each turn O inductance of the solenoidA coil of 15 turns and a radius of (R=10.0) cm surrounds a long solenoid of radius 2.00 cm and 1012 turns/ meter as in the figure. The current in the solenoid changes as I=6 sin(120t). Find the magnitude of induced emf ( in units of mV) at any given time t. 15-turn coil R I Select one: O A. 0.14 cos(120t) OB. 1.15 cos(120t) OC. 5.50 cos(120t) OD. 17.26 cos(120t) OE. 431.48 cos(120t)The magnetic flux through each turn of a 190-turn coil is given by g = 7.25 x 10-3 sin(wt), where w is the angular speed of the coil and g is in webers. At one instant, the coil is observed to be rotating at a rate of 9.40 x 10² rev/min. (Assume that t is in seconds.) (a) What is the induced emf in the coil as a function of time for this angular speed? (Use the following as necessary: t. Do not use other variables, substitute numeric values. Assume that is in volts. Do not include units in your answer.) E = (b) What is the maximum induced emf in the coil for this angular speed?Compute the induced EMF in the small circular loop of wire centered at x=x0 and y=y0 on x-y plane resulting from the time varying magnetic diplole directed into the direction of z located on z axis at z=z0. The dipole moment of m of magnetic dipole is m = m, cos(ot) . The radius of small circular loop of wire is r1.(r1<A 30-turn circular coil of radius 4.00 cm and resistance 1.000 is placed in a magnetic field directed perpendicular to the plane of the coil. The magnitude of the magnetic field varies in time according to the expression B = 0.010 Ot+ 0.040 Of, where B is in teslas and tis in seconds. Calculate the induced emf in the coil at t = 5.00 s.The principle of induction heating is explored in this problem. A sheet of metal (good conductor) of conductivity oc is inserted into AC magnetic field whose value at the surface z =+d and wwww H(d) = (-unitvector y) 10 A/m H(-d) = (-unitvector y) 20 A/m Determine the expressions for (a) the magnetic field vector field H (z) and (b) the volume current density field J (z) in the field region -dA uniform magnetic field B is perpendicular to the plane of a circular wire loop of radius r and with resistance R. The magnitude of the field varies with time according to B = B0e-t/T, where B0and T are constants (T is time constant). (a) Find an expresssion for the emf induced in the loop as a function of time. (b) If the loop lies in the plane of the page and the magnetic field initially points out of the page, then what is the magnitude and direction of the induced current in the loop, i.e., is it clockwise, counter-clockwise, or is there no current induced in the loop? Include a diagram for this situation.conducting rod with length L = 24.5 cm is being pulled along a ong u-shape conductor with negligible resistance, as shown in the figure below. If the uniform magnetic field in the figure has a constant value of 31.6 mT and the constant speed at which the vertical rod is being pulled is 8.31 m/s, the induced emf along the rod has a magnitude that is most nearly (A) 0.107 mV. (B) 32.1 mV. (C) 64.1 mV. (D) 0.929 mV. 6 of 15 (E) 4110 mV.SEE MORE QUESTIONSRecommended textbooks for youCollege PhysicsPhysicsISBN:9781305952300Author:Raymond A. Serway, Chris VuillePublisher:Cengage Learning
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