# Cheap Scale Reveals Coulomb’s Law

Measure the force between a charged object and a metal sphere.  Then use the force and distance to estimate the charge using Coulomb’s Law.

###### Basic Idea of the Experiment

Place a lightweight metalized ball on an electronic balance.  The scale registers any changes in the force on the ball.  A charged rod held over the ball induces an opposite charge in the ball, because the ball is grounded to the scale.  It is not a bad approximation to assume the charges are equal and opposite point charges, separated by the distance between the top of the ball and the bottom of the charged rod.  Use Coulomb’s law to calculate the amount of charge.  Vary the distance to show the inverse square law.

###### Materials for Coulomb’s Law Experiment:
• Scales: Electronic balances having 0.1 or 0.01 gram sensitivity are now available at low-cost — in the range of \$25.   The balance pan is actually grounded by the internal circuitry, and intentional grounding seems unnecessary.
• Metalized ball: Use styrofoam balls from craft stores. Wrapped in aluminum foil, these weigh several grams.
• Plastic rod: PVC plumbing pipe holds a good charge and costs pennies per linear foot. We used 1″ OD pipe.
• Fur for rubbing the pipe: Common scientific supplies.  If these seem overpriced, an old wool sock works fine.
###### Experimental procedure:
1.  Place ball on balance pan and press the tare button to zero the balance. Rub the end of the plastic rod with fur or wool, and hold it about 4 cm above the ball. Record the weight reading.
2.  Discuss with students why the reading is negative — that is, the force between the positive ball and negative rod is attractive.   If conditions favor static charge, the ball may roll around the balance pan — making the attraction obvious.
3.  Charge the plastic rod once, and quickly get the weight readings for a sequence of different distances between ball and rod — say, 3 cm , 6 cm and 9 cm.   Students will be able to demonstrate a rapidly decreasing attraction as distance increases.
###### Calculations and Discussion
•  The scale reads in grams.  Convert to kilograms and multiply by g = 10 m/s2 to get the force in Newtons:

F =kq2/r2

Solve the force equation for q.  For example, if the scale reads -0.5 gram for a distance of 4 cm, this gives q = [(.0005 x 10 x .042/(9 x 109 ) ]1/2  = 30 nC  .  A few tens of nanocoulombs is about as much charge as one produces in the classroom, while the class van der Graaf machine accumulates a couple of hundred nC.

• Discuss the inverse power law for force dependence on distance for fixed amount of charge.  If the weight loss is multiplied by r2, for the same charge and different r’s, the product should be constant. This proves the Coulomb force is an inverse square law.
###### Related Questions
1. The configuration used in this experiment is not unlike a charge cloud hovering over a mountain top.  Suppose the cloud contains 1.0 C of + charge, and this induces an equal and opposite charge on the mountain top.  Assuming the cloud is 1000 m above the mountain, what is the Coulomb force between the cloud and the mountain?
2. Exercise:  Draw in the E-field lines between the plastic rod and the metal sphere, showing where these lines originate and terminate, and showing the direction they point.
3. [Advanced topic]  Note it is only an approximation to assert that the charge induced in the aluminum ball is equal to the charge on the plastic pipe.  This assertion is probably true within an order of magnitude.  Therefore the calculation of ± q on either the ball or the rod would  be accurate within half an order of magnitude.