Physics Laboratory 5

Electric potentials and fields

In this laboratory you will explore the connection between electric field lines and equipotential surfaces.  Objects with net electric charge attract or repel each other.  If you want to change the position of a charged object relative other charged objects, you, in general, have to do (positive or negative) work.  But sometimes it is possible to move a charged object relative to other charged objects along a surface without doing any work.  The potential energy of the charged object does not change as you move it.  If an electric charge can travel along a surface without the electric field doing any positive or negative work, then the surface is called an equipotential surface.

Open a Microsoft Word document to keep a log of your experimental procedures and results.  Complete all the tasks (in blue).  Answer all questions.


Activity 1

The concept of work

image(a)  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. 

image(b)  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. 

Work and the electric field

imageIn 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.
(c)  A particle with charge +qe travels along a straight line from point W to point X.

image(d)  A particle travels from point X to point Z along the circular arc shown. 

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. 
(e)  Suppose the charge in part (c) increases from +qe to +1.7 qe.

(f)  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.

When a net force does work on an object, its kinetic energy changes.
Wnet = ½m(vf2 - vi2) = ∆K.
(g)  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. 

image

(h) Assume you have a test charge at rest at a distance of 2 cm from the charge on the right.  You want to move it.

What path could you choose, so you would not have to do any work?   What is the shape of the equipotential surface?   (Remember that in general you can move in three dimensions.)  Explain your reasoning.

image(i)  Find some equipotential surfaces for the charge configuration shown on the right, which consists of two charged metal plates placed parallel to each other.

What is the shape of the equipotential surfaces?  Remember you are trying to decide how a test charge could move so that the electric field does no work on it.  Sketch your predictions and explain your reasoning.

image(j)  Find some equipotential surfaces for the electric dipole charge configuration shown on the right.

Sketch your predictions and explain your reasoning.


Activity 2

You now will calculate the electric potential at grid points in the in the x-y plane due to two small, uniformly-charged spheres.  You will fix the position of the charged sphere with charge q2 and vary the position of the other charged sphere with charge q1.  The x-y plane is divided into a 26 x 26 grid. The upper left corner of the grid corresponds to x = -12.5 m, y = 12.5 m, and the lower right corner corresponds to x = 12.5 m, y = -12.5 m.  The charged spheres can be placed anywhere on the grid in the x-y plane, as well as above or below the x-y plane.  You will calculate the potential at each grid point and construct a surface and a contour plot of the potential.  The contour plots will display the equipotential lines.  The electric field is perpendicular to the equipotential lines, E = -V.  You will draw field lines indicating the direction and relative magnitude of the electric field in the vicinity of the charged spheres and calculate the magnitude of the electric field at selected points.

The potential at r = (x,y,z) outside a uniformly charged sphere centered at r' = (x', y', z') is

 V(r) =  kq/|r - r'| = kq/((x - x'2) + (y - y'2) + (z - z'2))½.

The constant k has a value of 9*109 in SI units.  If we measure q in units of nC = 109 C, then kq = 9 q Nm2/C.


Procedure:

Charge q2 is fixed at the origin.  Both charges have the same magnitude.  You can move the charge q1 to different positions with the scrollbars.  You can change the sign of charge q1 with the checkbox.



Convert your log into a lab report.

Name:
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Laboratory 5 Report

Save your Word document (your name_lab5.docx), go to Canvas, Assignments, Lab 5, and submit your document.