Answer to Question #87762 in Electricity and Magnetism for Nicholas Legault

Question

A group of students are recreating Millikan’s Oil Drop experiment in which a charged oil droplet is suspended in the electric field created by two horizontal charged plates. The droplet experiences a downward force due to gravity and an upward force due to the electrostatic force from the charges. The forces are balanced so that the droplet does not accelerate. In this case, the two horizontal parallel plates are 0.80 cm apart. A sphere of mass 2.73 x 10–13 kg remains stationary when the potential difference between the plates is 315 V with the upper plate negative.

Draw the FBD of the oil droplet.

Is the sphere positively or negatively charged? Explain how you know.

Calculate the magnitude of charge on the sphere.

How much excess or deficit of electrons does the sphere have?

Answer 1

Draw the FBD of the oil droplet.

Is the sphere positively or negatively charged? Explain how you know.

The upper plate is negative and therefore acts on a positively charged ball (F_E)

Answer: Sphere is positively charged

Calculate the magnitude of charge on the sphere.

The electric force (FE) and gravity (Fg) act on sphere and these forces are equal in value:

$$F_E= F_g (1)$$

Using (1) we got:

$$qE=mg (2)$$

where q is the charge on the oil drop and E is the electric field between the plates.

For parallel plates

$$E=\frac {V}{r} (3)$$

where V is the potential difference and r is the distance between the plates.

We put (3) in (2):

$$q\frac {V}{r}=mg (4)$$

Using (4) we got:

$$q=\frac {mgr}{V}$$

q=6.8×10^-17 C

Answer:

6.8×10^-17 C

How much excess or deficit of electrons does the sphere have?

Deficit of electrons:

$$\frac {6.8×10^{-17} C }{1.6×10^{-19} C}=425$$

Answer:

425