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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 high electron mobility transistor (HEMT) controls large currents by applying a small voltage to a thin sheet of electrons. The density and mobility of the electrons in the sheet are critical for the operation of the HEMT. HEMTs consisting of AlGaN/GaN/Si are being studied because they promise better performance at higher powers, temperatures, and frequencies than conventional silicon HEMTs can achieve. In one study, the Hall effect was used to measure the density of electrons in one of these new HEMTs. When a current of \(10.0 \mu\) A flows through the length of the electron sheet, which is \(1.00 \mathrm{~mm}\) long, \(0.300 \mathrm{~mm}\) wide, and \(10.0 \mathrm{nm}\) thick, a magnetic field of \(1.00 \mathrm{~T}\) perpendicular to the sheet produces a voltage of \(0.680 \mathrm{mV}\) across the width of the sheet. What is the density of electrons in the sheet?

A conducting rod of length \(L\) slides freely down an inclined plane, as shown in the figure. The plane is inclined at an angle \(\theta\) from the horizontal. A uniform magnetic field of strength \(B\) acts in the positive \(y\) -direction. Determine the magnitude and the direction of the current that would have to be passed through the rod to hold it in position on the inclined plane.

A proton with an initial velocity given by \((1.0 \hat{x}+$$2.0 \hat{y}+3.0 \hat{z})\left(10^{5} \mathrm{~m} / \mathrm{s}\right)\) enters a magnetic field given by \((0.50 \mathrm{~T}) \hat{z}\). Describe the motion of the proton

It would be mathematically possible, for a region with zero current density, to define a scalar magnetic potential analogous to the electrostatic potential: \(V_{B}(\vec{r})=-\int_{\vec{r}_{0}}^{\vec{r}} \vec{B} \cdot d \vec{s},\) or \(\vec{B}(\vec{r})=-\nabla V_{B}(\vec{r}) .\) However, this has not been done. Explain why not.

The magnetic field in a region in space (where \(x>0\) and \(y>0\) ) is given by \(B=(x-a z) \hat{y}+(x y-b) \hat{z},\) where \(a\) and \(b\) are positive constants. An electron moving with a constant velocity, \(\vec{v}=v_{0} \hat{x},\) enters this region. What are the coordinates of the points at which the net force acting on the electron is zero?
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