5.6.3: Problems

Exercise \(\PageIndex{1}\): Identify the poles of a square magnet

You can move the compass around. You can also move the gray magnet by dragging it at the pink square (position is given in centimeters). Restart. Determine the poles of the magnet. The colored blocks are there for your reference.

Problem authored by Anne J. Cox.
Script by Morten Brydensholt and modified by Anne J. Cox.

Exercise \(\PageIndex{2}\): Identify field-line diagram

The animation shows four wires carrying current (each wire carries current either into or out of the screen). Drag the compass around to map out the magnetic field in the left-hand panel. Restart.

Which of the three configurations (in the right-hand panel) shows the correct field lines for the original animation? Click inside the configuration (in the right-hand panel) to draw magnetic field lines.

Problem authored by Anne J. Cox.

Exercise \(\PageIndex{3}\): Identify correct trajectory of particle moving through a magnetic field

A positively charged particle moves through a uniform magnetic field. The animations show the field vectors (position is given in millimeters and time is given in seconds). Restart. Which animation is correct? Explain.

Problem authored by Anne J. Cox.

Exercise \(\PageIndex{4}\): Force on moving charges in a current carrying wire: find the direcion of the field

The animation illustrates charged particles flowing through a wire (position is given in millimeters and time is given in seconds). A current consists of charges moving (\(1\text{ C/s} = 1\) ampere) through a conducting wire. Remember that in a conductor, charges are free to move in response to forces. Initially, there is no magnetic field in the region shown. The particles travel in one direction. Restart.

1. What is the direction of the current in each case?
2. What is the direction of the magnetic field in each case?

Problem authored by Morten Brydensholt and modified by Anne J. Cox.

Exercise \(\PageIndex{5}\): Force on current carrying wire

This problem has two parts. You must first answer (a) before you can go on to answer (b). Restart.

1. Determine the poles of the horseshoe magnet. You can move the compass around.
2. After completing part (a), determine which animation shows the correct force on a wire carrying current out of the computer screen. You can drag the wire around in the animations.

Problem authored by Anne J. Cox.
Script authored by Morten Brydensholt and modified by Anne J. Cox.

Exercise \(\PageIndex{6}\): Rank magnetic fields that an electron moves through

An electron is shot through four regions of constant magnetic field (position is given in centimeters and time is given in seconds). Restart.

1. In which direction is the magnetic field in each region?
2. Rank the magnitude of the magnetic fields of the four regions, from smallest to greatest.
3. How would the path change if we inverted the direction of the magnetic field in every region? Draw the new path of the electron.
4. If you wanted to ensure that the particle did not enter Region II, would you increase or decrease the speed of the electron entering Region I? Give a mathematical proof of your answer.

Problem authored by Dwain Desbien and Melissa Dancy.

Exercise \(\PageIndex{7}\): Rank charges as they move through magnetic field

Six objects (all with a mass of \(5\) grams) are shot into a region of constant magnetic field. The blue object has a charge of \(6\text{ mC}\). The position and velocity of the blue object are given in the table (position is given in centimeters and time is given in seconds). All objects are located at \(x = - 50\text{ cm}\) at time \(t = 0\text{ s}\). Restart.

1. Rank the objects based on their velocity when they first encounter the magnetic field, from lowest to highest.
2. How does the magnitude of the velocity of each object change as it interacts with the magnetic field?
3. Rank the objects based on their charge, from lowest to highest.
4. What are the direction and magnitude of the magnetic field?

Problem authored by Melissa Dancy.

Exercise \(\PageIndex{8}\): Mass spectrometer

The animation shows a particle passing through a mass spectrometer (position is given in meters and time is given in seconds). There is a constant magnetic field throughout the region directed into the screen. There is a constant electric field in the first region only. Restart.

1. Is the particle charged? How do you know? If it is charged, does it have a positive or negative charge? Justify your answer.
2. If the electric field produced by the charged plates in the first region is \(80\text{ N/C}\), what is the value of the magnetic field in that region?
3. What is the charge-to-mass ratio (\(q/m\)) of the particle?

For an introduction to the mass spectrometer see Exploration 27.3.

Problem authored by Melissa Dancy.

Exercise \(\PageIndex{9}\): Velocity selector

The animation shows a \(30\text{-mg}\) charged object entering a region where a magnetic field and/or electric field can be applied (position is given in centimeters and time is given in seconds). The magnitude of the charge is \(4\times 10^{-3}\text{ C}\). Restart.

1. Is the object positively or negatively charged? Explain.
2. What is the magnitude of the electric field?
3. What is the magnitude of the magnetic field?
4. What voltage must be applied to the plates to create the electric field?

For an introduction to the velocity selector see Exploration 27.2.

Problem authored by Melissa Dancy.

Exercise \(\PageIndex{10}\): Find the mass of the current carrying rod in a magnetic field

The blue rod has a current flowing through it and sits in a uniform external magnetic field that points out of the page (as represented by the gray circles with white dots). The probe at the top records the force required to support the rod (position is given in centimeters, magnetic field is given in tesla, current is given in amperes, and force is given in newtons). Restart.

1. In which direction does the current flow through the rod?
2. What is the mass of the rod?

Problem authored by Anne J. Cox.

Physlets were developed at Davidson College and converted from Java to JavaScript using the SwingJS system developed at St. Olaf College.