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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 × 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 × 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 copper wire with density \(\rho=8960 \mathrm{~kg} / \mathrm{m}^{3}\) is formed into a circular loop of radius \(50.0 \mathrm{~cm} .\) The cross-sectional area of the wire is \(1.00 \cdot 10^{-5} \mathrm{~m}^{2},\) and a potential difference of \(0.012 \mathrm{~V}\) is applied to the wire. What is the maximum angular acceleration of the loop when it is placed in a magnetic field of magnitude \(0.25 \mathrm{~T}\) ? The loop rotates about an axis through a diameter.

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 \(1.00 \mathrm{~m}\).)

Which of the following has the largest cyclotron frequency? a) an electron with speed \(v\) in a magnetic field with magnitude \(B\) b) an electron with speed \(2 v\) in a magnetic field with magnitude \(B\) c) an electron with speed \(v / 2\) in a magnetic field with magnitude \(B\) d) an electron with speed \(2 v\) in a magnetic field with magnitude \(B / 2\) e) an electron with speed \(v / 2\) in a magnetic field with magnitude \(2 B\)

In the Hall effect, a potential difference produced across a conductor of finite thickness in a magnetic field by a current flowing through the conductor is given by a) the product of the density of electrons, the charge of an electron, and the conductor's thickness divided by the product of the magnitudes of the current and the magnetic field. b) the reciprocal of the expression described in part (a). c) the product of the charge on an electron and the conductor's thickness divided by the product of the density of electrons and the magnitudes of the current and the magnetic field. d) the reciprocal of the expression described in (c). e) none of the above.

An alpha particle \(\left(m=6.6 \cdot 10^{-27} \mathrm{~kg}, q=+2 e\right)\) is accelerated by a potential difference of \(2700 \mathrm{~V}\) and moves in a plane perpendicular to a constant magnetic field of magnitude \(0.340 \mathrm{~T}\), which curves the trajectory of the alpha particle. Determine the radius of curvature and the period of revolution.
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