(a)
The magnetic field at the surface of the inner conductor.
(a)
Answer to Problem 75AP
The magnetic field at the surface of the inner conductor is
Explanation of Solution
Write the expression for power.
Her,
Rewrite the above equation for
Write the expression for magnetic field.
Here,
Substitute
Conclusion:
Substitute
Further solve the above equation.
Therefore, magnetic field at the surface of the inner conductor is
(b)
The magnetic field at the inner surface of the outer conductor.
(b)
Answer to Problem 75AP
The magnetic field at the inner surface of the outer conductor is
Explanation of Solution
Conclusion:
Substitute
Further solve the above equation.
Therefore, magnetic field at the inner surface of the outer conductor is
(c)
The energy stored in the magnetic field in the space between the conductors in a
(c)
Answer to Problem 75AP
The energy stored in the magnetic field in the space between the conductors is
Explanation of Solution
Write the expression for energy stored in the magnetic field.
Here,
Substitute,
Conclusion:
Substitute
Substitute
Therefore, the energy stored in the magnetic field in the space between the conductors is
(d)
The pressure exerted on the outer conductor due to the current in the inner conductor.
(d)
Answer to Problem 75AP
The pressure exerted on the outer conductor due to the current in the inner conductor is
Explanation of Solution
Consider a small rectangular section of the outer cylinder of length
Write the expression for the force.
Here,
Substitute
Write the expression for pressure.
Here,
Substitute
Conclusion:
Substitute
Therefore, the pressure exerted on the outer conductor due to the current in the inner conductor is
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Chapter 32 Solutions
Physics: for Science.. With Modern. -Update (Looseleaf)
- A Figure P32.74 shows an N-turn rectangular coil of length a and width b entering a region of uniform magnetic field of magnitude Bout directed out of the page. The velocity of the coil is constant and is upward in the figure. The total resistance of the coil is R. What are the magnitude and direction of the magnetic force on the coil a. when only a portion of the coil has entered the region with the field, b. when the coil is completely embedded in the field, and c. as the coil begins to exit the region with the field?arrow_forwardReview. The use of superconductors has been proposed for power transmission lines. A single coaxial cable (Fig. P23.73) 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 be 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. P23.73arrow_forwardShow that Equation 32.28 in the text Ls Kirchhoffs loop rule as applied to the circuit in Figure P32.56 with the switch thrown to position b.arrow_forward
- When a wire carries an AC current with a known frequency, you can use a Rogowski coil to determine the amplitude Imax of the current without disconnecting the wire to shunt the current through a meter. The Rogowski coil, shown in Figure P23.8, simply clips around the wire. It consists of a toroidal conductor wrapped around a circular return cord. Let n represent the number of turns in the toroid per unit distance along it. Let A represent the cross-sectional area of the toroid. Let I(t) = Imax sin t represent the current to be measured. (a) Show that the amplitude of the emf induced in the Rogowski coil is Emax=0nAImax. (b) Explain why the wire carrying the unknown current need not be at the center of the Rogowski coil and why the coil will not respond to nearby currents that it does not enclose. Figure P23.8arrow_forwardA current-carrying conductor PQ of mass m and length L is placed on an inclined plane with angle of inclination (Fig. P30.93). A uniform magnetic field B is directed upward as shown. Assume friction is negligible. a. Determine the magnitude and direction of the current in the conductor so that it remains in equilibrium. b. If the direction of the current is reversed, will the conductor still be in equilibrium? If not, find the magnitude of the initial acceleration of the conductor. FIGURE P30.93arrow_forwardReview. Figure P31.31 shows a bar of mass m = 0.200 kg that can slide without friction on a pair of rails separated by a distance = 1.20 m and located on an inclined plane that makes an angle = 25.0 with respect to the ground. The resistance of the resistor is R = 1.00 and a uniform magnetic field of magnitude B = 0.500 T is directed downward, perpendicular to the ground, over the entire region through which the bar moves. With what constant speed v does the bar slide along the rails?arrow_forward
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