BackEach turn of a solenoid is a current loop with a magnetic dipole moment. Consider a 200-turn cylindrical solenoid that has an interior volume of 40 cm3 and for which each turn is a magnetic dipole moment with magnitude 8.0 x 10-4 A m2. What is the magnetic field strength inside the solenoid?
The earth's magnetic field, with a magnetic dipole moment of 8.0 x 1022 A m2, is generated by currents within the molten iron of the earth's outer core. Suppose we model the core current as a 3000-km-diameter current loop made from a 1000-km-diameter 'wire.' The loop diameter is measured from the centers of this very fat wire. What is the current density J in the current loop?
The heart produces a weak magnetic field that can be used to diagnose certain heart problems. It is a dipole field produced by a current loop in the outer layers of the heart. What is the magnitude of the heart's magnetic dipole moment?
A flat, circular disk of radius R is uniformly charged with total charge Q. The disk spins at angular velocity ω about an axis through its center. What is the magnetic field strength at the center of the disk?
In FIGURE P31.32, a circular loop of radius r travels with speed v along a charged wire having linear charge density λ. The wire is at rest in the laboratory frame, and it passes through the center of the loop. What electric and magnetic fields would an experimenter in the loop's frame calculate at distance r from the current of part c?
A solenoid 25.0 cm long and with a cross-sectional area of 0.500 cm2 contains 400 turns of wire and carries a current of 80.0 A. Calculate: the total energy contained in the coil's magnetic field (assume the field is uniform);
A thin 12-cm-long solenoid has a total of 370 turns of wire and carries a current of 2.0 A. Calculate the field inside the solenoid near the center.
(I) A 32-cm-long solenoid, 1.8 cm in diameter, is to produce a 0.30-T magnetic field at its center. If the maximum current is 5.4 A, how many turns must the solenoid have?
A 650-turn horizontal solenoid is 15 cm long. The current in its loops is 38 A. A straight wire cuts through the center of the solenoid, along a 3.0-cm diameter. This wire carries a 22-A current downward (and is connected by other wires that don’t concern us). What is the force on this wire assuming the solenoid’s field points due east?
The magnetic field B at the center of a circular coil of wire carrying a current I (as in Fig. 27–9) is B = (μ₀NI) / 2r where N is the number of loops in the coil and r is its radius. Imagine a simple model in which the Earth’s magnetic field of about 1 G ( = 1 x 10⁻⁴ T) near the poles is produced by a single current loop around the equator. Roughly estimate the current this loop would carry.
(III) Start with the result of Example 28–11 for the magnetic field along the axis of a single circular loop of wire carrying a dc current I to obtain the field along the central axis inside a very long solenoid with n turns per meter (Eq. 28–4) that stretches from +∞ to −∞ .
A small solenoid (radius ra) is inside a larger solenoid (radius rb > ra). They are coaxial with na and nb turns per unit length, respectively. The solenoids carry the same current, but in opposite directions. Let r be the radial distance from the common axis of the solenoids. If the magnetic field inside the inner solenoid (r < ra) is to be in the opposite direction as the field between the solenoids (ra < r < rb), but have half the magnitude, determine the required ratio nb/na.
A set of Helmholtz coils (see Problem 62, Fig. 28–61) have a radius R = 10.0 cm and are separated by a distance R = 10.0 cm. Each coil has 85 loops carrying a current I = 2.0 A. Determine the total magnetic field B along the 𝓍 axis (the center line for the two coils) in steps of 0.2 cm from the center of one coil (𝓍 = 0) to the center of the other (𝓍 = R).
A set of Helmholtz coils (see Problem 62, Fig. 28–61) have a radius R = 10.0 cm and are separated by a distance R = 10.0 cm. Each coil has 85 loops carrying a current I = 2.0 A. By what % does B vary from 𝓍 = 5.0 cm to 𝓍 = 6.0 cm?
A set of Helmholtz coils (see Problem 62, Fig. 28–61) have a radius 𝑅 = 10.0 cm and are separated by a distance 𝑅 = 10.0 cm . Each coil has 85 loops carrying a current I = 2.0 A. Graph B as a function of 𝓍.