Chapter 28: Problem 16
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 16
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 freeAn electromagnetic doorbell has been constructed by wrapping 70 turns of wire around a long, thin rod, as shown in the figure. The rod has a mass of \(30.0 \mathrm{~g}\), a length of \(8.00 \mathrm{~cm},\) and a cross-sectional area of \(0.200 \mathrm{~cm}^{2}\). The rod is free to pivot about an axis through its center, which is also the center of the coil. Initially, the rod makes an angle of \(\theta=25.0^{\circ}\) with the horizontal. When \(\theta=0.00^{\circ}\), the rod strikes a bell. A uniform magnetic field of 900. G is directed at an angle \(\theta=0.00^{\circ}\). a) If a current of \(2.00 \mathrm{~A}\) is flowing in the coil, what is the torque on the rod when \(\theta=25.0^{\circ} ?\) b) What is the angular velocity of the rod when it strikes the bell?
Consider an electron to be a uniformly dense sphere of charge, with a total charge of \(-e=-1.602 \cdot 10^{-19} \mathrm{C}\), spinning at an angular frequency, \(\omega\). a) Write an expression for its classical angular momentum of rotation, \(L\) b) Write an expression for its magnetic dipole moment, \(\mu\). c) Find the ratio, \(\gamma_{e}=\mu / L,\) known as the gyromagnetic ratio.
A long, straight wire is located along the \(x\) -axis \((y=0\) and \(z=0\) ). The wire carries a current of \(7.00 \mathrm{~A}\) in the positive \(x\) -direction. What are the magnitude and the direction of the force on a particle with a charge of \(9.00 \mathrm{C}\) located at \((+1.00 \mathrm{~m},+2.00 \mathrm{~m}, 0),\) when it has a velocity of \(3000 . \mathrm{m} / \mathrm{s}\) in each of the following directions? a) the positive \(x\) -direction b) the positive \(y\) -direction c) the negative \(z\) -direction
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 it levitated at the distance \(2.00 \mathrm{~mm}\) above the lower coil.
The wires in the figure are separated by a vertical distance \(d\). Point \(B\) is at the midpoint between the two wires; point \(A\) is a distance \(d / 2\) from the lower wire. The horizontal distance between \(A\) and \(B\) is much larger than d. Both wires carry the same current, \(i\). The strength of the magnetic field at point \(A\) is \(2.00 \mathrm{mT}\). What is the strength of the field at point \(B ?\)
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