A long solenoid has a diameter of 12.0 cm. When a current i exists in its windings, a uniform magnetic field of magnitude B = 43.6 mT is produced in its interior. By decreasing i, the field is caused to decrease at the rate of 6.67 mT/s. Calculate the magnitude of the induced electric field (a) 2.95 cm and (b) 9.54 cm from the axis of the solenoid. (a) Number i Units (b) Number i Units
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- 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 2In the figure, a conducting rectangular body of dimensions d, = 6.28 m., d, = 3.98 m. and d, = 1.37 m moves at constant velocity V %3D (23.5 m/s)i through a uniform magnetic fieldB =(45.2 mT)j. (a) What is the resulting electric field within the body, in unit-vector notation? (b) What is the resulting potential difference across the body? %3DA 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. =
- 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, counterclockwiseA 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 UnitsAn electron is moving at a speed of 1.40 × 104 m/s in a circular path of radius of 2.9 cm inside a solenoid. The magnetic field of the solenoid is perpendicular to the plane of the electron's path. The solenoid has 25 turns per centimeter. (a) Find the strength of the magnetic field inside the solenoid. Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully. μT (b) Find the current in the solenoid. mA
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