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Chapter 20: Q1Q (page 851)

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?

Short Answer

Expert verified

The parallel component of velocity will be unaffected by the magnetic field. The proton will follow a spiral path upwards around the magnetic field.

Step by step solution

01

Given data

A proton has a component of velocity parallel to the magnetic field as well as perpendicular to it.

02

Magnetic force

Magnetic force on a moving charge is directly proportional to the cross product of the velocity vector and the magnetic field.

03

Determination of the magnetic effect on the parallel component of the velocity and the net trajectory of the photon

Since the cross products of two parallel vectors is zero, the parallel component of the velocity of the proton along the magnetic field is unaffected by it. The perpendicular component faces the magnetic force and traces a circle around the magnetic field direction. Thus, the proton follows a spiral path with the parallel component moving up and the perpendicular component tracing a circle.

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Most popular questions from this chapter

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 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 E鈫�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.


In Figure 20.128 on the left is a region of uniform magnetic field B1into the page, and adjacent on the right is a region of uniform magnetic field B2 also into the page. The magnetic field B2is smaller than B1(B2<B1) . 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鈥檛 accelerate but moves with a constant speed.

Calculate this constant speed v in terms of the known quantities B1, B2, w, h, R and F , and explain your calculation carefully. Also show the approximate surface-charge distribution on the loop.

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).

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In which direction will conventional current flow through the resistor in Figure 20.87? What will be the direction of the magnetic force on the moving bar?

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 鈭�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 B鈫� , in terms of the known quantities shown in figure 20.101. Explain all steps in your reasoning.
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