5.1.2: Explorations
- Page ID
- 32777
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Exploration 1: Equilibrium
Two fixed charges and a dragable test charge are placed as shown (position is given in meters and force is given in newtons). The blue arrow represents the force on the red test charge. The forces on the fixed charges are not shown. You can examine the forces with the first fixed charge, with the second fixed charge, or with both fixed charges in place. Notice that the net force on the test charge is displayed in the yellow message box when you have only one charge present but not when you have both charges present. Restart.
Answer the following questions with both fixed charges in place.
- Determine the net force on the test charge at the point (\(3\text{ m},\: 4\text{ m}\)).
- Determine the net force on the test charge at a point midway between the two charges.
- Is (are) there any point(s) where the net force on the test charge is zero? If so, find those points.
- What is the ratio of the charges?
Exploration 2: Explore the Effect of Multiple Charges
A positive test charge is shown in the animation. You can add positive and/or negative charges. All charges are added to the middle of the animation, so you must drag each newly added charge to a new location. When you push "play," the test charge will move under the influence of the forces from the other charges. Restart.
- Add one positive charge. Describe and explain the motion of the test charge.
- How can you tell from its motion that the test charge experiences a force, but that the force decreases as the test charge moves away from the positive charge?
- What do you predict the motion will be if the positive charge is replaced by a negative charge?
- Clear the screen and try it. Was your prediction correct?
- How can you configure two charges of the same sign and keep the test charge stationary? Describe your configuration.
- What happens if you move one of the charges slightly? This is a demonstration of an unstable equilibrium point (like a gymnast on a balance beam; nudge her one way or the other and she will fall).
- Design and describe a configuration in which the test charge will oscillate back and forth.
- Explain why (in terms of the forces) the test charge oscillates in your configuration.
- Clear the charges and add one negative charge. Let the test charge start moving (so it has an initial velocity) and then move the negative charge around so that the test charge orbits the negative charge. Explain (in terms of forces) why it orbits.
Exploration 3: Electrostatic Ranking Task
Study the motion of a positively charged test object under the action of five fixed charges. Run the animation a number of times starting with the test object in different positions. Before you move the particle, you must push "reset" (otherwise the particle will simply continue along the same trajectory as before). Note that the motion can be quite complicated depending on your choice of initial position (position is given in meters and time is given in seconds). Rank the fixed charges from most negative to most positive. Restart.
- To begin with, start the test charge close to each individual charge separately to determine the signs of the different charges. Which ones are positive, negative, or neutral?
You will need to use a systematic approach to rank the negative and positive charges. For the positive charges, you might put the test charge fairly close and then watch the motion (and the trail).
- Which positive charge provides a bigger force to the test charge?
For the negative charges, put the charge a little way above the unknown negative charge and watch it approach.
- Which one of the negative charges provides a bigger force?
- How do you know?
- Using this approach, rank the charges.
Exploration 4: Dipole Symmetry
Each animation shows a positive charge (red) along with two unknown charges (blue). The electrical force on the positive charge is represented with a force vector. You can drag the red charge along a portion of the \(x\) axis (position is given in meters and force is given in \(\text{[newtons}/k\text{]}\), where \(k\) is the constant in Coulomb's law). Restart.
- In which animation are the two unknown charges a positive and negative charge of equal magnitude?
- Qualitatively speaking, what charge configuration would produce the results in the other two animations?
- For the animation with a positive and a negative charge of equal magnitude, what is the value of the magnitude of the two blue charges if the red charge is \(2.5\text{ coulombs}\)?
Exploration authored by Melissa Dancy
Exploration 5: Pendulum Electroscope
Two identical balls are hung pendulum-like in a laboratory as shown (position is given in meters and time is given in seconds). The charge on each ball, in \(mC\), can be varied by using the slider. Position can be measured by click-dragging. Restart.
- Is there any difference in behavior if the on both balls charge is changed from negative to positive?
- Notice that you can zero the velocity. Can you find a spot where the balls are in equilibrium? (You may need to set the velocity to zero several times to get the balls in equilibrium.)
- What is the mass of each ball? (Assume that the charge on the two balls is uniformly distributed.)
- How large a charge is required for the angle (as measured from the pivot) between the two balls in equilibrium to be \(90\) degrees? How large a charge for \(180\) degrees?
Exploration 6: Run Coulomb's Gauntlet
A positive test charge is shown in the animation. You can add positive and/or negative charges. All charges are added to the middle of the animation, so you must drag each newly added charge to a new location. When you push "play," the test charge will move under the influence of the forces from the other charges. Restart.
Move the charges so that the test charge can make it from its starting place to the finish line without hitting a wall.
- Describe your technique.
- What is it about the Coulomb force that makes this so difficult? Explain.
Physlets were developed at Davidson College and converted from Java to JavaScript using the SwingJS system developed at St. Olaf College.