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A rod of length L = 10.0 cm that is forced to move at constant speed v = 5.00 m/s along horizontal rails. The rod, rails, and connecting strip at the right form a conducting loop. The rod has resistance 0.400 Ω; the rest of the loop has negligible resistance. A current i = 100 A through the long straight wire at distance a = 10.0 mm from the loop sets up a (nonuniform) magnetic field through the loop. Find the (a) emf and (b) current induced in the loop. (c) At what rate is thermal energy generated in the rod? (d) What is the magnitude of the force that must be applied to the rod to make it move at constant speed? (e) At what rate does this force do work on the rod?

L R = 5.00 Q X Xix x 1 |X X X X R P = FexV =8.50 J/s Fext W X xx x X X X X X X X X A rectangular wire loop of length L, width w, is pulled out of a constant, uniform magnetic field with constant velocity v. The loop has a resistance R. The magnetic field of magnitude B, points into the plane of the paper, and is confined to the rectangular region shown above. Work must be done on the loop at the rate of P, to move it through the magnetic field at constant velocity. Find the magnitude of the emf, & and the current I for the loop.

A solenoid in your car is 36 cm long and has a diameter of 7.9 cm. It is made of copper wire with a radius of 0.50 mm. The turns are closely packed and form a single layer. Assume the resistivity of copper is 1.68 ✕ 10−8 Ω · m. (a) When the solenoid is connected to your battery with E  = 11.6 V, what is the magnetic field inside the solenoid? (Enter the magnitude.)  T

Find the flux of the Earth's magnetic field of magnitude 5.00 ✕ 10-5 T, through a square loop of area 30.0 cm2 for the following. (a) when the field is perpendicular to the plane of the loop T·m2(b) when the field makes a 30.0° angle with the normal to the plane of the loop T·m2(c) when the field makes a 90.0° angle with the normal to the plane T·m2

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A square wire loop (side length 1.5 m) is oriented so that it is perpendicular to an external magnetic field B, with half the area of the loop embedded in the field, as shown below. The loop contains a battery with a constant emf Eb = 7.2 V and a resistor R = 3.2 Ω. The external magnetic field is B(t) = [0.027 T − (0.56 T/s) t] î where î is out of the page. (a) Findtheemfproducedbyinductionintheloop. (b) Findthenetcurrentintheloopfromboththeinducedemfandthebattery. (c) What direction is the current in? (a) Findtheemfproducedbyinductionintheloop. (b) Findthenetcurrentintheloopfromboththeinducedemfandthebattery. (c) What direction is the current in? (a) Find the emf produced by induction in the loop. (b) Find the net current in the loop from both the induced emf and the battery. (c) What direction is the current in?

A time-dependent uniform magnetic field of magnitude B (t) is confined in a cylindrical region of radius R. A conducting rod of length 2D is placed in the region, as shown. Show that the magnitude of the emf between the ends of the rod is given by dB ε = D√R²-D² dt P₁1 B(t) 2D R

A loop of wire with radius r=0.025m is placed in a region of uniform magnetic field with magnitude B. As shown in the figure, the field direction is perpendicular to the plane of the loop. The magnitude of the magnetic field changes at a constant rate from B1=0.65T to B2=6.5T in time Δt=3.5s. The resistance of the wire is R=15Ω. Part (a)  Calculate, in Tesla squared meters, the magnitude of the change in the magnetic flux.  Part (b)  Calculate, in volts, the average EMF induced in the loop.  Part (c)  Calculate, in amperes, current induced in the loop.

The figure below shows a bar of mass m = 0.240 kg that can slide without friction on a pair of rails separated by a distance { = 1.20 m and located on an inclined plane that makes an angle e = 35.0° with respect to the ground. The resistance of the resistor is R = 1.50 N and a uniform magnetic field of magnitude B = 0.500 T is directed downward, perpendicular to the ground, over the entire region through which the bar moves. With what constant speed v does the bar slide along the rails? m/s