4. Using one of the equations in Ampere's Law which is B=(2Trr), prove that at any point inside the pipe, the magnitude of magnetic field is zero when the current flows along the length of an infinitely long, straight, thin-walled pipe.
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- 5. This time the loop has constant area 0.780 m^2, and the magnetic field has constant strength 0.550 T. This time we re going to achieve an induced voltage 0.278 V by rotating the loop through a 90 degree angle. How much time must it take for the loop to complete this 90 degree turn? 2.16 s 1.54 s 0.77 s 1.23 s5. A rectangular loop of wire (length L=13.0 cm and width W=7.80 cm) is moving as shown in the drawing with a speed of 1.00 m/s. The loop is leaving a region in which a 2.80 T magnetic field exists; the magnetic field outside this region is zero. During a time of 0.13 s, what is the magnitude of the change in the magnetic flux? Wb XXXX XXX XXXXXXXXX xxxxxxxxx xxxxxxxxx XXXXXXXXX XX7. A conducting loop has an area of 280 cm² and resistance 15 . It is perpendicular to a spatially uniform magnetic field and carries a 350 mA of induced current. At what rate is the magnetic field changing?
- 2. Suppose that a rectangular toroid has 2000 windings, h = 1 cm, an inner radius of R1 = 4 cm, and an outer radius of R2 = 6 cm. What is the current flowing through the toroid when the energy in its magnetic field is 2.0 x 10-6 J?2. The figure below shows a 99-turn square coil rotating about a vertical axis at at ? = 1,520 rev/min. The length of a side of the coil is 20.0 cm. The horizontal component of the Earth's magnetic field at the coil's location is equal to 2.00 ✕ 10−5 T. a) What is the magnitude of the maximum emf (in mV) induced in the coil by the Earth's magnetic field? mV b) What is the orientation of the coil with respect to the magnetic field when the maximum emf occurs? The plane of the coil is oriented 45° with respect to the magnetic field. The plane of the coil is perpendicular to the magnetic field. The plane of the coil is parallel to the magnetic field.3. The thin, uniform rod shown below has negligible mass and and a length of 0.200 m. It is attached to the floor by a frictionless hinge at point P. A horizontal spring with force constant k = 4.80 N/m connects the other end of the rod to a vertical wall. The rod is in a uniform magnetic field of B = 0.340 T directed into the plane of the page. There is a current of /= 6.50 A in the rod, as shown. a. Calculate the torque due to the magnetic force on the rod for an axis at point P. Do this by defining a differential magnetic force on the rod for a differential length dr at an arbitrary distance r from point P. Relate this differential magnetic force to its differential torque at point P. Then sum (i.e., integrate) the contributions from the entire length of the rod to get the total torque on the rod. b. Consider Hooke's Law, which states that the force exerted by the spring when stretched or compressed a length x is Fspring = kx. Now, given that the rod makes an angle of 53.0° with the…
- 5. A solenoid has 500 turns, radius = 4 cm. and length = 16 cm, carries a current of 25 amps. What is the magnetic field inside the solenoid? What is the total flux inside the solenoid?1. Two solenoids have the same number of turns per unit length, n, and same current i flowing through them. The diameter of coil (a) is twice that of coil (b). If which coil is the magnetic field strength bigger? O A OB A. Coil (a) B. Coil (b) C. The magnetic field is the same in both. D. Not enough information O C ANNAMAANA wwwwwwwwwww. No, that's not the correct answer. (a) X (b)3. A metal strip 6.5 cm long and 0.85 cm wide moves with constant velocity v through a uniform magnetic field with B = 0.0012 T pointing into the page, as shown in the figure. A potential dif- ference of 3.9 µV is measured between points x and y. (a) Which point has the higher potential, x or y? Briefly explain your reasoning. y x B (b) Calculate the speed v necessary to produce the potential difference given above.
- 4. A rectangular coil of wire (a = 28.0 cm, b = 36.0 cm) containing a single turn is placed in a uniform 4.80 T magnetic field, as the drawing shows. The current in the loop is 12.0 A. Determine the magnitude of the magnetic force on the right side of the loop. oof19 o0 19 0of19 oof19 009 oof19 dookig oof19 a oof19 0of19o B 19. 0of19 oof19.of19 oof19.0 0of19 0of19 c3. A zero-resistance rod of length 14.4 cm is being pushed along zero-resistance wires in a region where a uniform magnetic field of strength 2.00 T is directed out of the page as shown. If the wires and rod complete a circuit through a 2.90 N resistor then what velocity will the rod maintain if it is subjected to a constant pushing force of 22.0 N? Zero-resistance wires Push