Chapter 28: Problem 12
Discuss how the accuracy of a compass needle in showing the true direction of north can be affected by the magnetic field due to currents in wires and appliances in a residential building.
Chapter 28: Problem 12
Discuss how the accuracy of a compass needle in showing the true direction of north can be affected by the magnetic field due to currents in wires and appliances in a residential building.
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Get started for freeSuppose that the magnetic field of the Earth were due to a single current moving in a circle of radius \(2.00 \cdot 10^{3} \mathrm{~km}\) through the Earth's molten core. The strength of the Earth's magnetic field on the surface near a magnetic pole is about \(6.00 \cdot 10^{-5} \mathrm{~T}\). About how large a current would be required to produce such a field?
When a magnetic dipole is placed in a magnetic field, it has a natural tendency to minimize its potential energy by aligning itself with the field. If there is sufficient thermal energy present, however, the dipole may rotate so that it is no longer aligned with the field. Using \(k_{\mathrm{B}} T\) as a measure of the thermal energy, where \(k_{\mathrm{B}}\) is Boltzmann's constant and \(T\) is the temperature in kelvins, determine the temperature at which there is sufficient thermal energy to rotate the magnetic dipole associated with a hydrogen atom from an orientation parallel to an applied magnetic field to one that is antiparallel to the applied field. Assume that the strength of the field is \(0.15 \mathrm{~T}\)
Two identical coaxial coils of wire of radius \(20.0 \mathrm{~cm}\) are directly on top of each other, separated by a 2.00 -mm gap. The lower coil is on a flat table and has a current \(i\) in the clockwise direction; the upper coil carries an identical current and has a mass of \(0.0500 \mathrm{~kg} .\) Determine the magnitude and the direction that the current in the upper coil has to have to keep the coil levitated at its current height.
A toy airplane of mass \(0.175 \mathrm{~kg}\), with a charge of \(36 \mathrm{mC}\), is flying at a speed of \(2.8 \mathrm{~m} / \mathrm{s}\) at a height of \(17.2 \mathrm{~cm}\) above and parallel to a wire, which is carrying a 25 - A current; the airplane experiences some acceleration. Determine this acceleration.
Can an ideal solenoid, one with no magnetic field outside the solenoid, exist? If not, does that render the derivation of the magnetic field inside the solenoid (Section 28.4) void?
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