A long solenoid has a diameter of 13.2 cm. When a current i exists in its windings, a uniform magnetic field of magnitude B = 28.1 mT is produced in its interior. By decreasing i, the field is caused to decrease at the rate of 5.92 mT/s. Calculate the magnitude of the induced electric field (a) 4.23 cm and (b) 9.63 cm from the axis of the solenoid.
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- A rectangular loop of wire with dimensions 1.50 cm by 8.00 cm and resistance R = 0.600 is being pulled to the right out of a region of uniform magnetic field. The magnetic field has magnitude B = 3.50 T and is directed into the plane of figure, see below. At the instant when the speed of the loop is |v|= 3.00 m/s and it is still partially in the field region, what force (magnitude and direction) does the magnetic field exert on the loop?A rectangular loop of area A = 0.150 m2 is placed in a region where the magnetic field is perpendicular to the plane of the loop. The magnitude of the field is allowed to vary in time according to B = 0.550e−t/2.00, where B is in teslas and t is in seconds. The field has the constant value 0.550 T for t < 0. What is the value for e m f at t = 8.000 s?Figure (a) shows an element of length ds = 1.26 um in a very long straight wire carrying current. The current in that element sets up a differential magnetic field aB at points in the surrounding space. Figure (b) gives the magnitude dB of the field for points 3.6 cm from the element, as a function of angle between the wire and a straight line to the point. The vertical scale is set by dB = 60.0 pT. What is the magnitude of the magnetic field set up by the entire wire at perpendicular distance 3.6 cm from the wire? Number i Units dB (pT) dB₂ 0 μT (a) π/2 9 (rad) (b) Wire 2
- A circular coil of 479 winds of wire (radius 8.6 cm, resistance = 1.4 M) is placed in a uniform magnetic field that is perpendicular to the plane of the loop. The magnitude of the field changes with time according to B = 10 sin (8t) mT, where t is measured in seconds. Determine the magnitude of the current induced in the loop at t=s. =Extremely large magnetic fields can be produced using a procedure called flux compression. A metallic cylinder tube of radius R is placed coaxially in a long solenoid of slightly larger radius. The space between the solenoid and the tube is filled with a highly explosive material. When the explosive is detonated, it causes the tube to implode into a cylinder of radius r < R. If the implosion happens too quickly, the current induced in the tube maintains an almost constant magnetic flux within it. If the initial magnetic field on the solenoid is 2.50 T and R/r = 12.0, what is the maximum value that the magnetic field can reach? (Answer in T and up to the units house)A solid conducting bar is free to move across two ends of a conducting U shape of wire that are separated by L=25 cm. On the base of the U shape is a resistor R=20 ohms. The whole apparatus is in a constant magnetic field B=0.7 T pointing out of the page. If the conducting bar has negligent resistance itself and is moved to the right at a constant velocity of 12 m/s, what is the magnitude and direction of the current induced in the loop? a) 0.11 A, clockwise b) 0.11 A, counterclockwise c) 2.1 A, clockwise d) 2.1 A, counterclockwise
- A long solenoid has a diameter of 11.0 cm. When a current i exists in its windings, a uniform magnetic field of magnitude B = 31.1 mT is produced in its interior. By decreasing i, the field is caused to decrease at the rate of 9.57 mT/s. Calculate the magnitude of the induced electric field (a) 2.88 cm and (b) 7.42 cm from the axis of the solenoid. (a) Number Units (b) Number i UnitsA rectangular loop of area A = 0.150 m2 is placed in a region where the magnetic field is perpendicular to the plane of the loop. The magnitude of the field is allowed to vary in time according to B = 0.550e−t/2.00, where B is in teslas and t is in seconds. The field has the constant value 0.550 T for t < 0. What is the value for at t = 8.000 s?A rectangular loop (l = 1.5 cm, w = 1 cm) lies vertically, parallel to the z-axis. A uniform magnetic field of 0.5 T goes through the loop by making an angle 0 = 20° with the normal to the loop. Find the magnetic flux through the loop. 2. Find the following if the magnetic field decreases to zero in an interval of time of 7 ms: (a) The direction of the induced current (b) The average induced emf Eavg (c) The average intensity lavg of the induced current if the wire making the loop has a resistance of 5 N. 1. W Normal to loop B
- You are given a straight piece of conductor that is 5.0 cm long and moves in a region of uniform magnetic field of 1.6 T along the z-direction. If the conductor is oriented along the x-axis and moves in the y-direction with a velocity of 5.0 m/s, find the magnitude of induced voltage that will be produced between the ends of this moving conductor.(a) A 17.0 m long, thin, uniform steel beam slides south at a speed of 29.0 m/s. The length of the beam maintains an east-west orientation while sliding. The vertical component of the Earth's magnetic field at this location has a magnitude of 44.0 µT. What is the magnitude of the induced emf between the ends of the beam (in mV)? mV (b) What If? The west end of the beam impacts and sticks to a pylon, causing the beam to rotate clockwise as viewed from above. While the beam rotates, what is the magnitude of the induced emf between the ends of the beam (in mV)? (Hint: use conservation of angular momentum to find the speed of the beam after the collision.) mV