## Extra Credit 4

### Work and the electric field

Please complete the exercises below and answer all questions.  Then go to Canvas, Extra credit 4, and enter your answers to selected questions.

A: The concept of work

The work W done on an object by a constant force is defined as W = Fd.  It is equal to the magnitude of the force, multiplied by the distance the object moves in the direction of the force.
The SI unit of work is Nm = J.
An object travels from point A to point B while two constant forces of equal magnitude are exerted on it, as shown in the figure on the right.

• Is the work done on the object by F1 positive, negative, or zero?
• Is the work done on the object by F2 positive, negative, or zero?
• Is the net work done on the object positive, negative, or zero?

An object travels from point A to point B while two constant forces of unequal magnitude are exerted on it, as shown in the figure on the right.

• Is the work done on the object by F1 positive, negative, or zero?
• Is the work done on the object by F2 positive, negative, or zero?
• Is the net work done on the object positive, negative, or zero?

B: Work and the electric field

In the diagram on the right the red dot denotes a positive point charge.  Points W, X, Y, and Z and the point charge lie in the same plane.  Points W and Y are equidistant from the charge, as are points Y and Z.
Draw the electric field vectors at points W, X, Y, and Z.
A particle with charge +qe travels along a straight line from point W to point X.

• Is the work done by the electric field on the particle positive, negative, or zero?
Explain using a sketch that shows the electric force on the particle and the displacement of the particle.

A particle travels from point X to point Z along the circular arc shown.

• Is the work done by the electric field on the particle positive, negative, or zero?  Explain!
Hint:  Sketch the direction of the force on the particle and the direction of the displacement for several short intervals during the motion.
• Compare the work done by the electric field when the particle travels from point W to point X to that done when the particle travels from point W to point Z along the path shown on the right.

C: Electric potential difference

A potential energy function is a function of the position of an object.  It can only be defined for conservative forces.  A force is conservative if the work it does on an object depends only on the initial and final position of the object and not on the path.
Suppose the charge in part B increases from +qe to +1.7 qe.

• Is the work done by the electric field as the particle travels from from W to X greater than, less than, or equal to the work done by the electric field on the original particle.  Explain!
• How is the quantity "the work divided by the charge" affected by this change?

The electric potential difference  ∆VWX between two points W and X is defined to be the negative of the work done by the electric field on a charge q, divided by q, as q travels from W to X.

• Does this quantity depend on the magnitude of the charge that is used?  Explain!
• Does this quantity depend on the sign of the charge that is used?  Explain!

When a net force does work on an object, its kinetic energy changes.
Wnet = ½m(vf2 - vi2) = ∆K.
A particle of charge |qe| = 2*10-6 C and mass m = 3*10-8 kg is released from rest at point W.  The speed of the particle is measured to be 40 m/s as it passes point X.

• Is qe positive or negative?  Explain!
• What is the change in the kinetic energy of the particle as it travels from point W to point X?
• Find the work done on the particle by the electric field between points W and X.
• What is the electric potential difference ∆VWX = VW - VX between points W and X?

Now go to Canvas, Assignments, Extra Credit 4.  Use the simulation to help you answer questions 1 - 5.  You can submit twice and the highest score counts.