** 12. A flexible copper cable forms a conducting loop in the presence of a magnetic field of strength 5.0 x 10-3 T into the page, as shown at left. The ends of the wire pass through a narrow rubber ring and are finally attached to a 10-2 resistor. The resistor is then pulled downward, pulling the wire through the ring and reducing the size of the loop. Assume that the resistor is carefully pulled at a speed so that the area of the loop diminishes at a rate of 0.10 m²/s. a) What emf is induced in the wire? b) In which direction, clockwise or counterclockwise, will the induced current start to flow in the wire loop? ww Pull c) Assuming the resistance of the copper cable is negligible, what is the current through the resistor?

The superconducting magnet of an MRI scanner requires 810 A of current to create a magnetic field of 4.5 T in the center of its solenoid coil with a 0.65 m radius.    If the solenoid is 1.9 m long, how many loops of wire does it have?  N =

A piece of copper wire has a resistance per unit length of 8.70 x 10 o/m. The wire is wound into a thin, flat coil of many turns that has a radius of 0.146 m. The ends of the wire are connected to a 12.0-V battery. Find the magnetic field strength at the center of the coil. Number Units

An air-core solenoid with 64 turns is 8.00 cm long and has a diameter of 1.20 cm. When the solenoid carries a current of 0.710 A, how much energy is stored in its magnetic field?

A circular coil of wire of 200 turns and diameter 5 cm carries a current of 4 A. It is placed in a magnetic field of 0.70 T with the plane of the coil making an angle of 30° with the magnetic field. What is the torque on the coil? 2.5 N·m 1.8 N.m 0.48 N.m 0.95 N·m

As a new electrical technician, you are designing a large solenoid to produce a uniform 0.120-T magnetic field near the center of the solenoid. You have enough wire for 4000 circular turns. This solenoid must be 55.0 cm long and 2.80 cm in diameter. What current will you need to produce the necessary field?  Express your answer to three significant figures and include the appropriate units.

A circular coil enclosing an area of 140 cm? is made of 210 turns of copper wire (shown in the figure below). The wire making up the coil has no resistance; the ends of the wire are connected across a 3.00-N resistor to form a closed circuit. Initially, a 1.20-T uniform magnetic field points perpendicularly upward through the plane of the coil. The direction of the field then reverses so that the final magnetic field has a magnitude of 1.20 T and points downward through the coil. If the time interval required for the field to reverse directions is 0.200 s, what is the average current in the coil during that time? R

A conducting rod spans a gap of length L = 0.085 m and acts as the fourth side of a rectangular conducting loop, as shown in the figure. A constant magnetic field B = 0.55 T pointing into the paper is in the region. The rod is moving under an external force with an acceleration a = At?, where A = 4,5 m/s*. The resistance in the wvire is R = 145 Q. L = 0.085 m B = 0.55 T A = 4,5 m/s R= 145 N B X X R V X X Express the magnitude of the magnetic flux going through the loop, , in terms of B, x and L. Express the speed of the rod, v, in terms of A and t. Assume v = 0 at t = 0. Express the position of the rod, x, in terms of 4 and t. Assume x = 0 at 1 = 0. Express the derivative of the magnetic flux, do/dt, in terms of B, 4, L and t. do/dt = Express the magnitude of the emf induced in the loop, ɛ, in terms of B, L, A and t. Express the current induced in the loop, I, in terms of ɛ and R. Calculate the numerical value of I at t = 2s in A. I(t=2s) = www

A conducting bar of length moves to the right on two frictionless rails as shown in the figure below. A uniform magnetic field directed into the page has a magnitude of 0.310 T. Assume R = 8.70 and l = 0.340 m. l R * xxxxxx x x X x counterclockwise into the page out of the page x x x Bin (a) At what constant speed should the bar move to produce an 8.20-mA current in the resistor? m/s (b) What is the direction of the induced current? clockwise (c) At what rate is energy delivered to the resistor? mW

= The figure shows a solid metal object moving through a uniform magnetic field given by B (7.00 x 10-2T) k. The motion creates a potential difference of 1.30 x 103 V across the object, with the (unseen) bottom face negatively charged. What is the speed (m/s) of the object? d₁=5.00 x 102 m, d2= 3.00 x 102 m, d3 = 2.00 × 10² m. A do ds