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Chapter 27: Problem 17

An electron is traveling horizontally from the northwest toward the southeast in a region of space where the Earth's magnetic field is directed horizontally toward the north. What is the direction of the magnetic force on the electron?

Short Answer

Expert verified
Answer: The direction of the magnetic force on the electron is downward.

Step by step solution

01

Understand the given information and problem

We know an electron is traveling horizontally in the Earth's magnetic field. Due to their negative charge, moving electrons experience a force within a magnetic field (Lorentz force). Determine the force's direction.
02

Identify the directions of movement and magnetic field

The electron is moving from the northwest to the southeast. The Earth's magnetic field points horizontally towards the north.
03

Apply the left-hand rule or right-hand rule for electrons

Remember, we use the left-hand rule for electrons, contrary to the right-hand rule of conventional current flow. To apply the left-hand rule, stretch your left hand with thumb, index, and middle fingers perpendicular to each other. Your thumb represents the electron's motion, your index finger represents the magnetic field, and your middle finger represents the magnetic force.
04

Align your left hand with the movement and magnetic field

Point your thumb along the direction of electron movement, from the northwest toward the southeast. Point your index finger in the direction of the magnetic field, which is horizontally towards the north.
05

Observe the middle finger's direction

After aligning your thumb and index finger according to the electron movement and the magnetic field, your middle finger will point downward. This indicates that the magnetic force on the electron is in the downward direction. So, the direction of the magnetic force on the electron is downward.

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Most popular questions from this chapter

A particle with charge \(q\) is at rest when a magnetic field is suddenly turned on. The field points in the \(z\) -direction. What is the direction of the net force acting on the charged particle? a) in the \(x\) -direction b) in the \(y\) -direction c) The net force is zero. d) in the \(z\) -direction

Show that the magnetic dipole moment of an electron orbiting in a hydrogen atom is proportional to its angular momentum, \(L: \mu=-e L / 2 m,\) where \(-e\) is the charge of the electron and \(m\) is its mass.

The Earth is showered with particles from space known as muons. They have a charge identical to that of an electron but are many times heavier \(\left(m=1.88 \cdot 10^{-28} \mathrm{~kg}\right)\) Suppose a strong magnetic field is established in a lab \((B=0.50 \mathrm{~T})\) and a muon enters this field with a velocity of \(3.0 \cdot 10^{6} \mathrm{~m} / \mathrm{s}\) at a right angle to the field. What will be the radius of the resulting orbit of the muon?

A semicircular loop of wire of radius \(R\) is in the \(x y\) -plane, centered about the origin. The wire carries a current, \(i\), counterclockwise around the semicircle, from \(x=-R\) to \(x=+R\) on the \(x\) -axis. A magnetic field, \(\vec{B}\), is pointing out of the plane, in the positive \(z\) -direction. Calculate the net force on the semicircular loop.

An electron with energy equal to \(4.00 \cdot 10^{2} \mathrm{eV}\) and an electron with energy equal to \(2.00 \cdot 10^{2} \mathrm{eV}\) are trapped in a uniform magnetic field and move in circular paths in a plane perpendicular to the magnetic field. What is the ratio of the radii of their orbits?
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