5.1.3: Problems

Exercise \(\PageIndex{1}\): Like and unlike charges

Five charged objects are shown on the screen along with vectors representing the forces on each object. You can click-drag on any object to change its position (position is given in meters). Restart.

1. Find two objects that repel each other and place them aside. Can you find any object that is attracted to one of these objects and repelled by the other? What does this observation tell you?
2. How many charges are alike?

Exercise \(\PageIndex{2}\): Positive and negative

Four charged objects are shown on the screen along with vectors representing the forces on each object. You can click-drag on any object to change its position (position is given in meters). Restart.

What, if anything, is wrong with the animation?

Exercise \(\PageIndex{3}\): Net charge

In the animation the electrostatic force on each charge is indicated by an arrow (position is given in meters). The magnitude of each charge is \(1\text{ C}\), and the blue charge is negative. What is the net charge shown in the animation? Restart.

Problem authored by Wolfgang Christian, Melissa Dancy, and Chuck Bennett.

Exercise \(\PageIndex{4}\): Two hidden charges

A positive charge (red) is shown along with a region blocked by a gray curtain (position is given in meters). The electric force on the positive charge is represented with a force vector. The region behind the gray curtain contains two charges of equal magnitude but unknown polarity (unknown sign). You can drag the red charge along the black circle. Restart.

Draw a picture showing the sign and location of each charge within the covered area.

Problem authored by Melissa Dancy.

Exercise \(\PageIndex{5}\): Three hidden charges

A positive charge (red) is shown along with a region blocked by a gray curtain (position is given in meters). The electrostatic force on the positive charge is represented by a force vector. The region behind the gray curtain contains three charges of equal magnitude but unknown polarity (unknown sign). The charges are arranged in an equilateral triangle located around the center of the square. You can drag the red charge along the black circle. Restart.

Draw a picture indicating the sign and location of each charge within the covered area.

Problem authored by Melissa Dancy.

Exercise \(\PageIndex{6}\): "Tug of war"

In the animation there are two black fixed charges and a blue movable positive test charge (position is given in meters and force is given in newtons). The test charge has an attached arrow that indicates the direction and relative magnitude of the net electric force. The charge on the left is \(25\) times that of the right-hand charge. The initial separation is \(d = 8.0\text{ m}\). Drag the test charge and note that the force is displayed in the yellow message box. Restart.

For each configuration,

1. There is a single point at which the electric force on the test charge is zero. Find that point at which the separation of the two fixed charges is \(6\text{ m}\).
2. Does the animation provide sufficient information to calculate the charge on the two black objects? If so, calculate the charge in coulombs.
3. Find an expression for the position of zero force for any value of the charge separation. Show that your result agrees with the animation.

Problem authored by Chuck Bennett and Wolfgang Christian.

Exercise \(\PageIndex{7}\): Charge, inertia, and trajectories

An unknown green charge (with a \(#1\) on it) is shot into a region containing four fixed charges (numbered \(2--5\)), one of which is known to be positive (the red one). You can measure position using a mouse down (position is given in meters and time is given in seconds). Restart.

Determine the signs of the unknown charges. You may consider neutral as a possible answer. Justify your response.

Problem authored by Scott Bonham and modified by Melissa Dancy.

Exercise \(\PageIndex{8}\): Circular motion and charged objects

A positive test charge of \(1\times 10^{-5}\text{ C}\) with a mass of \(0.9\text{ kg}\) is shown near a variable charge with a fixed position (at the origin). You may change the charge of the central charge and the initial velocity of the test charge (position is given in meters and time is given in seconds). Restart.

Set the charge of the central charge to \(-20\times 10^{-5}\text{ C}\).

1. What initial velocity must you give the test charge so that the test charge can make it from its starting place to the finish line in a circular path?
2. For an arbitrary negative central charge, \(Q\), what initial velocity must you give the test charge so that the test charge can make it from its starting place to the finish line in a circular path? Your answer should be a formula for \(v\) in terms of \(Q\). When you have an answer, test it with \(Q = -10\times 10^{-5}\text{ C}\) and \(Q = -30\times 10^{-5}\text{ C}\).

Exercise \(\PageIndex{9}\): Discharge

Two conducting spheres of the same mass and volume are shown (position is given in meters and force is given in newtons). The magnitude of the force on a sphere is shown when you drag it. Restart.

Drag the spheres so that they make contact. What was the initial charge on each sphere?

Problem authored by Melissa Dancy and Wolfgang Christian.

Exercise \(\PageIndex{10}\): Electroscope

A charged ball with a mass of \(30\) grams is hung pendulum-like as shown (position is given in meters and time is given in seconds). A second ball with a negative charge of \(3\text{ mC}\) is placed on a wood table. Play the animation and move the ball on the table toward and away from the pendulum. Restart. What is the charge on the pendulum? (Assume that the charge on the two balls is uniformly distributed.)

Exercise \(\PageIndex{11}\): Coulomb force and spring force

A \(20\)-gram charged ball is connected to a spring and placed on a frictionless tabletop as shown (position is given in meters and time is given in seconds). Restart.

1. Find the equilibrium position.
2. Find the spring constant.

Add a \(2-\mu\text{C}\) charge on the right-hand side of the table.

3. Has the spring constant changed? Explain.
4. Find the new equilibrium position.
5. What is the charge on the ball?

Exercise \(\PageIndex{12}\): Charge on a tabletop

A charged ball of mass \(100\) grams is placed on a frictionless tabletop with a second charge fixed underneath. Play the animation and observe the motion. You may drag the charged ball to any position before beginning the animation. Restart.

If the charge of the fixed charge (beneath the table) is negative \(2\:\mu\text{C}\), determine the value of the charge on the ball. (Show hint.)

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