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Chapter 27: Problem 1

A magnetic field is oriented in a certain direction in a horizontal plane. An electron moves in a certain direction in the horizontal plane. For this situation, there a) is one possible direction for the magnetic force on the electron. b) are two possible directions for the magnetic force on the electron. c) are infinite possible directions for the magnetic force on the electron.

Short Answer

Expert verified
Answer: There are two possible directions for the magnetic force on the electron.

Step by step solution

01

Understand the nature of magnetic force

Magnetic force is experienced by charged particles like electrons, moving in a magnetic field. The force is given by the formula F = q(v 脳 B), where F is the force vector, q is the electric charge, v is the velocity vector of the particle, and B is the magnetic field vector. Here, the direction of the magnetic force is given by the cross product (v 脳 B), which means that the magnetic force will always act perpendicular to both the velocity vector and the magnetic field vector.
02

Identify the plane of motion for the electron

According to the problem, both the electron's motion and the magnetic field are in a horizontal plane.
03

Determine the direction of the magnetic force on the electron

Since the magnetic force is perpendicular to the plane formed by the velocity vector and the magnetic field vector, and both of these vectors lie in the horizontal plane, the only way for the magnetic force vector to be perpendicular to this plane is to point in either an upward or downward direction (vertically). Therefore, there are only two possible directions for the magnetic force to act on the electron.
04

Choose the correct option

Based on our analysis, the correct answer is: b) there are two possible directions for the magnetic force on the electron.

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Most popular questions from this chapter

A square loop of wire of side length \(\ell\) lies in the \(x y\) -plane, with its center at the origin and its sides parallel to the \(x\) - and \(y\) -axes. It carries a current, \(i\), in the counterclockwise direction, as viewed looking down the \(z\) -axis from the positive direction. The loop is in a magnetic field given by \(\vec{B}=\left(B_{0} / a\right)(z \hat{x}+x \hat{z}),\) where \(B_{0}\) is a constant field strength, \(a\) is a constant with the dimension of length, and \(\hat{x}\) and \(\hat{z}\) are unit vectors in the positive \(x\) -direction and positive \(z\) -direction. Calculate the net force on the loop.

In your laboratory, you set up an experiment with an electron gun that emits electrons with energy of \(7.50 \mathrm{keV}\) toward an atomic target. What deflection (magnitude and direction) would Earth's magnetic field \((0.300 \mathrm{G})\) produce in the beam of electrons if the beam is initially directed due east and covers a distance of \(1.00 \mathrm{~m}\) from the gun to the target? (Hint: First calculate the radius of curvature, and then determine how far away from a straight line the electron beam has deviated after \(1.00 \mathrm{~m}\).)

A particle with mass \(m\) and charge \(q\) is moving within both an electric field and a magnetic field, \(\vec{E}\) and \(\vec{B}\). The particle has velocity \(\vec{v},\) momentum \(\vec{p}\), and kinetic energy, \(K\). Find general expressions for \(d \vec{p} / d t\) and \(d K / d t\), in terms of these seven quantities.

An electron with a speed of \(4.0 \cdot 10^{5} \mathrm{~m} / \mathrm{s}\) enters a uniform magnetic field of magnitude \(0.040 \mathrm{~T}\) at an angle of \(35^{\circ}\) to the magnetic field lines. The electron will follow a helical path. a) Determine the radius of the helical path. b) How far forward will the electron have moved after completing one circle?

The work done by the magnetic field on a charged particle in motion in a cyclotron is zero. How, then, can a cyclotron be used as a particle accelerator, and what essential feature of the particle's motion makes it possible? A blue problem number indicates a worked-out solution is available in the Student Solutions Manual. One \(\bullet\) and two \(\bullet\) indicate increasing level of problem difficulty.
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