he figure below shows a bar of mass m = 0.270 kg that can slide without friction on a pair of rails separated by a distance ℓ = 1.20 m and located on an inclined plane that makes an angle ? = 29.5° with respect to the ground. The resistance of the resistor is R = 3.30 Ω, 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

In the figure, an electron with an initial kinetic energy of 3.80 keV enters region 1 at time t = 0. That region contains a uniform magnetic field directed into the page, with magnitude 0.0100 T. The electron goes through a half-circle and then exits region 1, headed toward region 2 across a gap of 30.0 cm. There is an electric potential difference AV = 2000 V across the gap, with a polarity such that the electron's speed increases uniformly as it traverses the gap. Region 2 contains a uniform magnetic field directed out of the page, with magnitude 0.0168 T. The electron goes through a half-circle and then leaves region 2. At what time t does it leave? Number i Units × B₁ Region 1 Region 2 OB₂

The loop in the figure has a resistance of 2.5 2 and is being pulled to the right at 1.0 m/s. X X X||X × X 2.0 T X||X 1.0 T 2.0 m X X X ||× × X X X X X • 2.0 m 2.0 m (a) Find the total magnetic flux through the loop, directed into the page, at the time instant shown. b)In the above problem, find the total magnetic flux through the loop, directed into the page, 2.0 s later. (c) In the above problem, find the magnitude of the induced current in the loop during this 2.0 s interval.

A loop of wire with radius r= 0.183 m is in a magnetic field of magnitude B as shown in the figure. The magnetic field is perpendicular to the plane of the loop. B changes from B1= 0.22 T to B2= 7.5 T in Δt = 7.5 s at a constant rate. (a)  Express the magnetic flux Φ going through a loop of radius r assuming a constant magnetic field B.  (b)  Express the change in the magnetic flux going through this loop, ΔΦ, in terms of B1, B2 and r.  (c) Express the magnitude of the average induced electric field, E, induced in the loop in terms of ΔΦ, r and Δt.

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

In the figure, an electron with an initial kinetic energy of 3.80 keV enters region 1 at time t = 0. That region contains a uniform magnetic field directed into the page, with magnitude 0.00620 T. The electron goes through a half-circle and then exits region 1, headed toward region 2 across a gap of 22.0 cm. There is an electric potential difference AV = 2000 V across the gap, with a polarity such that the electron's speed increases uniformly as it traverses the gap. Region 2 contains a uniform magnetic field directed out of the page, with magnitude 0.0157 T. The electron goes through a half-circle and then leaves region 2. At what time t does it leave? B₁ Region 1 Number i Units Region 2 OB₂

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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?

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