Figure a shows a circuit consisting of an ideal battery with emf $$\mathscr{E}=6.00\muV$$, a resistance R, and a small wire loop of area . For the time interval t = 10 s to t = 20 s, an external magnetic field is set up throughout the loop.The field is uniform, its direction is into the page in Figure a, and the field magnitude is given by , where B is in teslas, a is a constant, and t is in seconds. Figure b gives the current in the circuit before, during, and after the external field is set up. The vertical axis scale is set by . Find the constant a in the equation for the field magnitude.
From the datum at in Fig. b
we see which implies that the
resistance is
Now, the value of the current during
leads us to equate
This shows that the induced emf is . Now we use Faraday's law:
Plugging in and we
obtain
Figure shows a wire that has been bent into a circular arc of radius r = 24.0 cm, centered at O. A straight wire OP can be rotated about O and makes sliding contact with the arc at P. Another straight wire OQ completes the conducting loop. The three wires have cross-sectional area and resistivity , and the apparatus lies in a uniform magnetic field of magnitude B = 0.150 T directed out of the figure.Wire OP begins from rest at angle and has constant angular acceleration of . As functions of (in rad), find (a) the loops resistance and (b) the magnetic flux through the loop. (c) For what is the induced current maximum and (d) what is that maximum?
A rectangular coil of N turns and of length a and width b is rotated at frequency in a uniform magnetic field , as indicated in Figure . The coil is connected to co-rotating cylinders, against which metal brushes slide to make contact. (a) Show that the
emf induced in the coil is given (as a function of time t) by
This is the principle of the commercial alternating-current generator. (b) What value of Nab gives an emf with when the loop is rotated at 60.0 rev/s in a uniform magnetic field of 0.500 T?
In a given figure an isosceles triangle conducting wire is entering into the region of perpendicular uniform magnetic field with constant velocity . The magnitude of induced emf as a function of time(t) in the wire is(till side is outside the field)
A circular region in an xy plane is penetrated by a uniform magnetic field in the positive direction of the z axis.The field’s magnitude B (in teslas) increases with time t (in seconds) according to , where a is a constant. The magnitude E of the electric field set up by that increase in the magnetic field is given by Figure versus radial distance
r; the vertical axis scale is set by , and the horizontal axis scale is set by . Find a.
Figure a shows two concentric circular regions in which uniform magnetic fields can change. Region 1, with radius , has an outward magnetic field that is increasing in magnitude. Region 2, with radius , has an outward magnetic field that may also be changing.
Imagine that a conducting ring of radius R is centered on the two regions and then the emf around the ring is determined. Figure b gives emf as a function of the square of the rings radius, to the outer edge of region 2. The vertical axis scale is set by . What are the rates (a) and (b) ? (c) Is the magnitude of increasing, decreasing, or remaining constant?
