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Calculate the mobile electron density for nickel. A mole of nickel has a mass of 59g (0.059kg), and one mobile electron is released by each atom in metallic nickel. The density of nickel is about 8.8g/cm³, or$8.8×{10}^{3}kg/m^3$

Suppose that a proton has a component of velocity parallel to the magnetic field as well as perpendicular to it (Figure 20.80). What is the effect of the magnetic field on this parallel component of the velocity? What will the trajectory of the proton look like?

In the simple mass spectrometer shown in figure 20.101, positive ions are generated in the ion source. They are released traveling at very low speed, into the region between two accelerating plated between which there is potential difference $\mathbf{∆}\mathit{V}$ . In the shaded region there is negligible magnetic field. The semicircle traces the path of one single charged positive ion of mass M, which travels through the accelerating plates into the magnetic field region, and hits the ion detector as shown. Determine the appropriate magnitude and direction of the magnetic field $\stackrel{→}{\mathbf{B}}$ , in terms of the known quantities shown in figure 20.101. Explain all steps in your reasoning.

A long solenoid with diameter 4 cm is in a vacuum, and a lithium nucleus ( 4 neutrons and 3 protons ) is in a clockwise circular orbit inside the solenoid ( Figure 20.102 ). It takes \({\bf{50ns}}\,\left( {{\bf{50 \times 1}}{{\bf{0}}^{{\bf{ - 9}}}}{\bf{s}}} \right)\) for the lithium nucleus to complete one orbit.

In Figure 20.115 two long straight wires carrying a large conventional current I are connected by one-and-a-quarter turns of wire of radius $\mathit{R}$. An electron is moving to the right with speed v at the instant that it passes through the center of the arc. You apply an electric field $\stackrel{\mathbf{→}}{\mathbf{E}}$at the center of the arc in such a way that the net force on the electron at this instant is zero. (You can neglect the gravitational force on the electron, which is easily shown to be negligible, and the magnetic field of the coil is much larger than the magnetic field of the Earth.)

Determine the direction and magnitude of the electric field . Be sure to explain your work fully; draw and label any vectors you use.

A neutral iron bar is dragged to the left at speed v through a region with a magnetic field B points out of the page (Figure 20.122). Which diagram (1-5) best shows the state of the bar?

A neutral copper bar oriented horizontally moves upward through a region where there is a magnetic field out of the page. Which diagram (1-5) in Figure 20.123 correctly shows the distribution of charge on the bar?

A metal rod of length L slides horizontally at constant speed v on frictionless insulating rails through a region of uniform upward magnetic field of magnitude B (Figure 20.124).

On a diagram, show the polarization of the rod and the direction of the Coulomb electric field inside the rod. Explain briefly. What is the magnitude of the Coulomb electric field inside the rod? What is the potential difference across the rod? What is the emf across the rod? What are the magnitude and direction of the force you have to apply to keep the rod moving at a constant speed v?

In Figure 20.128 on the left is a region of uniform magnetic field ${\mathit{B}}_{\mathbf{1}}$into the page, and adjacent on the right is a region of uniform magnetic field ${\mathit{B}}_{\mathbf{2}}$ also into the page. The magnetic field ${\mathit{B}}_{\mathbf{2}}$is smaller than ${\mathit{B}}_{\mathbf{1}}\mathbf{(}{\mathbf{B}}_{\mathbf{2}}\mathbf{<}{\mathbf{B}}_{\mathbf{1}}\mathbf{)}$ . You pull a rectangular loop of wire of length w, height h, and resistance R from the first region into the second region, on a frictionless surface. While you do this you apply a constant force F to the right, and you notice that the loop doesn’t accelerate but moves with a constant speed.

Calculate this constant speed v in terms of the known quantities ${\mathit{B}}_{\mathbf{1}}$, ${\mathit{B}}_{\mathbf{2}}$, w, h, R and F , and explain your calculation carefully. Also show the approximate surface-charge distribution on the loop.

A bar magnet whose magnetic dipole moment is $\mathbf{15}{\mathbf{\text{‼î.³¾}}}^{\mathbf{\text{2}}}$is aligned with an applied magnetic field of $\mathbf{4}\mathbf{\text{â€Í¿}}$. How much work must you do to rotate the bar magnet $\mathbf{180}\mathbf{°}$to point in the direction opposite to the magnetic field?