One hundred turns of (insulated) copper wire are wrapped around a wooden cylindrical core of cross-sectional area . The two ends of the wire are connected to a resistor. The total resistance in the circuit is . If an externally applied uniform longitudinal magnetic field in the core changes from 1.60 T in one direction to 1.60 T in the opposite direction, how much charge flows through a point in the circuit during the change?
The charge flowing through a point in the circuit during the change in magnetic field is,
The magnetic flux through area A in a magnetic field is given by Faraday’s law of induction. If the magnetic field is perpendicular to the area A, then substitute the given values in the formula to find the charge.
Faraday's law of electromagnetic induction states, Whenever a conductor is placed in a varying magnetic field, an electromotive force is induced in it.
Formulae are as follows:
Where, is magnetic flux, N is number of turns, dt is time.
According to Faraday’s law,
From Ohm’s law, emf = i.R and i = dq/dt
Integrating this with respect to time,
To calculate the charge flowing through the point,
According to Faraday’s law, if the magnetic field is perpendicular to the area A, then,
Hence, the charge flowing through a point in the circuit during the change in magnetic field is,
Therefore, the charge flow through a point in the circuit during the change in the magnetic field can be found by using Faraday’s law.
Figure (a) shows, in cross section, two wires that are straight, parallel, and very long. The ratio of the current carried by wire 1 to that carried by wire 2 is . Wire 1 is fixed in place. Wire 2 can be moved along the positive side of the x-axis so as to change the magnetic energy density uB set up by the two currents at the origin. Figure (b) gives uB as a function of the position x of wire 2. The curve has an asymptote of , and the horizontal axis scale is set by . What is the value of (a) i1 and (b) i2?
A square wire loop with 2.00m sides is perpendicular to a uniform magnetic field, with half the area of the loop in the field as shown in Figure. The loop contains an ideal battery with emf . If the magnitude of the field varies with time according to , with B in Tesla and t in seconds, (a)what is the net emf in the circuit?(b)what is the direction of the (net) current around the loop?
The wire loop in Fig. 30-22a is subjected, in turn, to six uniform magnetic fields, each directed parallel to the axis, which is directed out of the plane of the figure. Figure 30- 22b gives the z components Bz of the fields versus time . (Plots 1 and 3 are parallel; so are plots 4 and 6. Plots 2 and 5 are parallel to the time axis.) Rank the six plots according to the emf induced in the loop, greatest clockwise emf first, greatest counter-clockwise emf last.
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