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Chapter 19: Problem 100

A strip of copper carries current in the \(+x\) -direction. There is an external magnctic field directed out of the page. What is the direction of the Hall electric field?

Short Answer

Expert verified
Answer: The direction of the Hall electric field is in the \(-y\) direction.

Step by step solution

01

Understanding the problem and setting up the coordinates

The magnetic field is given in the \(z\) direction, pointing out of the page. The current is in the \(x\) -direction, flowing through the copper strip. Our goal is to find the direction of the Hall electric field, which is perpendicular to both the current and the magnetic field.
02

Right-hand rule for the magnetic force on moving charges

We'll use the right-hand rule to determine the direction of the force experienced by the mobile charges as they move through the strip due to the external magnetic field. Place the thumb of your right hand in the direction of the current (in this case, the \(+x\) direction), and let your fingers curl in the direction of the magnetic field (coming out of the page, or in the \(+z\) direction). The direction in which your palm faces represents the direction of the force experienced by the positively charged particles (\(+q\)) in the copper strip. In this case, your palm will be facing in the \(+y\) direction.
03

Determine the direction of the Hall electric field

Now that we know the direction of the force experienced by the positive charges in the copper strip, we can conclude that the Hall electric field will be established in the opposite direction to this force. Therefore, the Hall electric field is in the \(-y\) direction. So the direction of the Hall electric field is in the \(-y\) direction.

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Most popular questions from this chapter

A uniform magnetic field of \(0.50 \mathrm{T}\) is directed to the north. At some instant, a particle with charge \(+0.020 \mu \mathrm{C}\) is moving with velocity \(2.0 \mathrm{m} / \mathrm{s}\) in a direction \(30^{\circ}\) north of east. (a) What is the magnitude of the magnetic force on the charged particle? (b) What is the direction of the magnetic force?
A certain fixed length \(L\) of wire carries a current \(I\) (a) Show that if the wire is formed into a square coil, then the maximum torque in a given magnetic field \(B\) is developed when the coil has just one turn. (b) Show that the magnitude of this torque is \(\tau=\frac{1}{16} L^{2} I B\)
In an electric motor, a circular coil with 100 turns of radius $2.0 \mathrm{~cm}$ can rotate between the poles of a magnet. When the current through the coil is \(75 \mathrm{~mA},\) the maximum torque that the motor can deliver is \(0.0020 \mathrm{~N} \cdot \mathrm{m} .\) (a) What is the strength of the magnetic field? (b) Is the torque on the coil clockwise or counterclockwise as viewed from the front at the instant shown in the figure?
Two identical bar magnets lic onatable along a straight line with their north poles facing each other. Sketch the magnetic field lines.
An electromagnet is made by inserting a soft iron core into a solenoid. The solenoid has 1800 turns, radius \(2.0 \mathrm{cm},\) and length $15 \mathrm{cm} .\( When \)2.0 \mathrm{A}$ of current flows through the solenoid, the magnetic field inside the iron core has magnitude 0.42 T. What is the relative permeability \(\overline{K_{\mathrm{B}}}\) of the iron core? (See Section 19.10 for the definition of \(\boldsymbol{K}_{\mathbf{B}} .\) )
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