5.2.3: Problems

Exercise \(\PageIndex{1}\): Find the unknown charge

A fixed particle with an unknown charge is shown along with a dragable test charge. The vectors shown point in the direction of the electric field, and the color of the vectors represent the field's magnitude (position is given in centimeters and electric field strength is given in newtons/coulomb). Restart.

1. Determine the unknown charge in coulombs.
2. Is the charge due to an excess of electrons or a deficit of electrons?
3. Calculate the number of electrons (excess or deficit) that are needed to produce the observed field.

Exercise \(\PageIndex{2}\): What is the net charge?

The electric field lines, due to four charged particles, are shown in the applet (position is given in meters). You can click-drag any of these particles. If you overlap two charges, their charge values will add. Restart.

Is the net charge of the distribution positive, negative, or zero?

Problem authored by Mario Belloni and Wolfgang Christian and modified by Melissa Dancy.

Exercise \(\PageIndex{3}\): Identify the hidden charge distribution

Five animations show the electric field produced by a configuration of hidden charges. The arrows represent the direction of the electric field, and the color represents the intensity of the field. Restart. Which electric field would be produced by the charge configuration shown below? Red represents a charge of \(+Q\) and blue represents a charge of \(-Q\).

a.  b.  c.  d.  e. 

Problem authored by Melissa Dancy.

Exercise \(\PageIndex{4}\): Rank the electric fields

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

1. What is the direction of the electric field in each region?
2. Rank the magnitude of the electric fields of the four regions, smallest to greatest.

Problem authored by Melissa Dancy.

Exercise \(\PageIndex{5}\): Rank the electric fields

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

1. What is the direction of the electric field in each region?
2. Rank the magnitude of the electric fields of the four regions, smallest to greatest.

Problem authored by Melissa Dancy.

Exercise \(\PageIndex{6}\): Find the electric field

An electron is shot into a region of constant electric field shown in green (position is given in centimeters and time is given in \(\mu\text{sec}\), \(10^{-6}\text{ s}\)). What are the magnitude and direction of the electric field? Restart.

Problem authored by Melissa Dancy.

Exercise \(\PageIndex{7}\): Find the electric field

An electron is shot through a region of constant electric field (time is given in \(\mu\text{sec}\) [\(10^{-6}\text{ s}\)] and position is given in centimeters). Restart.

1. Which vector most closely shows the direction of the electric field?
   
   Figure \(\PageIndex{1}\)
2. What is the magnitude of the electric field?

Problem authored by Melissa Dancy.

Exercise \(\PageIndex{8}\): Find the unknown charge

The charge on \(A\) is \(1\text{ nC}\) and the charge on \(B\) is \(-3\text{ nC}\) (position is given in meters and electric field strength is given in newtons/coulomb). Restart.

1. Where does the unknown charge (movable) need to be placed for the electric field at the origin (where the black dot is) to be zero?
2. What is the charge on the unknown charge?

Problem authored by Anne J. Cox.

Exercise \(\PageIndex{9}\): Equation for the electric field

Four point charges of equal strength but two different polarities are arranged on the corners of a square as shown. The strength of each charge is measured in \(\text{nC}\) and can be varied using the slider. You can mouse-down to read the magnitude of the field at any point in the animation (position is given in meters and electric field strength is given in newtons/coulomb). Restart.

Find a formula for the electric field midway between charge \(2\) and \(3\) (indicated by the small black dot) as a function of the strength of the charges. Include a vector diagram that also shows the direction of the resultant field.

Problem authored by Chuck Bennett and Wolfgang Christian.

Exercise \(\PageIndex{10}\): Find the electric field and charge of a uniformly charged rod

Derive an expression for the electric field as a function of position along the line shown (position is given in meters and force is given in newtons). Restart. If the purple test charge has a charge of \(1\:\mu\text{C}\), what is the total charge on the red rod in the animation?

1. Configuration I: Field along the axis of the red rod.
2. Configuration II: Field perpendicular to the red rod.

Remember that a test charge is defined as a charge that is so small that it does not influence other charges.

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.