c) Compute the numerical values of & and I at t = 0.1 s. (Partial answer: I = 35 A)

Review. The use of superconductors has been proposed for power transmission lines. A single coaxial cable (Fig. P31.47) could carry a power of 1.00 103 MW (the output of a large power plant) at 200 kV, DC, over a distance of 1.00 103 km without loss. An inner wire of radius a = 2.00 cm, made from the superconductor Nb3Sn, carries the current I in one direction. A surrounding superconducting cylinder of radius b = 5.00 cm would carry the return current I. In such a system, what is the magnetic field (a) at the surface of the inner conductor and (b) at the inner surface of the outer conductor? (c) How much energy would he stored in the magnetic field in the space between the conductors in a 1.00 103 km superconducting line? (d) What is the pressure exerted on the outer conductor due to the current in the inner conductor? Figure P31.47

A flip coil is a relatively simple device used to measure a magnetic field, It consists of a circular coil of N turns wound with fine conducting wire. The coil is attached to a ballistic galvanometer, a device that measures the total charge that passes through it. The coil is placed in a magnetic field B such that its face is perpendicular to the field. It is then flipped through 180°, and tire total charge Q that flows through the galvanometer is measured. (a) If the total resistance of tire coil and galvanometer Is R, what is the relationship between B and Q? Because the coil is very small, you can assume that Bis uniform over it. (b) How can you determine whether or not tire magnetic field is perpendicular to the face of the coil?

Unreasonable results Frustrated by the small Hall voltage obtained in blood flow measurements, a medical physicist decides to increase the applied magnetic field strength to get a 0.500-V output for blood moving at 30.0 cm/s in a 1.50-cm-diameter vessel. (a) What magnetic field strength is needed? (b) What is unreasonable about this result? (C) Which premise is responsible?

In a long, .straight, vertical lightning stroke, electrons move downward and positive ions move upward and constitute a current of magnitude 20.0 kA. At a location 50.0 m east of the middle of the stroke, a free electron drifts through the air toward the west with a speed of 300 m/s. (a) Make a sketch showing the various vectors involved. Ignore the effect of the Earth's magnetic field. (b) Find the vector force the lightning stroke exerts on the electron. (c) Find the radius of the electrons path. (d) Is it a good approximation to model the electron as moving in a uniform field? Explain your answer. (e) If it does not collide with any obstacles, how many revolutions will the electron complete during the 60.0-s duration of the lightning stroke?

The picture tube in an old black-and-white television uses magnetic deflection coils rather than electric deflection plates. Suppose an electron beam is accelerated through a 50.0-kV potential difference and then through a region of uniform magnetic field 1.00 cm wide. The screen is located 10.0 cm from the center of the coils and is 50.0 cm wide. When the field is turned off, the electron beam hits the center of the screen. Ignoring relativistic corrections, what field magnitude is necessary to deflect the beam to the side of the screen?

A proton having an initial velocity of 20.0iMm/s enters a uniform magnetic field of magnitude 0.300 T with a direction perpendicular to the protons velocity. It leaves the field-filled region with velocity 20.0jMm/s. Determine (a) the direction of the magnetic field. (b) the radius of curvature of the protons path while in the field, (c) the distance the proton traveled in the field, and (d) the time interval during which the proton is in the field.

Review. In Figure P30.42, a uniform magnetic field decreases at a constant rate dB/dt = K, where K is a positive constant. A circular loop of wire of radius a containing a resistance R and a capacitance C is placed with its plane normal to the field. (a) Find the charge Q on the capacitor when it is fully charged. (b) Which plate, upper or lower, is at the higher potential? (c) Discuss the force that causes the separation of charges. Figure P30.42

Figure 22.30 (Quick Quiz 22.6) Four closed paths around three current-carrying wires. Rank the magnitudes of Bds for the closed paths a through d in Figure 22.30, from greatest to least.

Two long, straight wires are parallel and 10 cm apart. One cans a current of 2.0 A, the other a current of 5.0 A. (a) If the two currents flow in opposite directions, what is the magnitude and direction of the force pet unit length of one wire on the other? (b) What is the magnitude and direction of the force per unit length if the currents flow in the same direction?