Investigating electric potential between two parallel plates and around a charged sphere using a flame probe

Potential around a charged sphere

8. The apparatus was set up as shown above. Ensure that the sphere was away from the walls and at least 0.5 m above the bench. A measuring tape was stuck on the bench to measure the distance of the probe from the sphere.  
9. The flame probe was placed close to, but not touching, the sphere and at the same level as the sphere’s centre.
10. The voltage of the EHT supply was adjusted until the electroscope gave the largest possible deflection.
11. The probe was moved away slowly, keeping it at the same level as the centre of the sphere. The deflection of the leaf was observed.
12. The probe was moved around the sphere, keeping it at a constant distance from the centre of the sphere. The deflection of the leaf was observed.
13. A meter ruler was attached on the bench, with its zero mark at the position vertically below the centre (located by dropping a piece of string with a mass attached).
14. The flame probe stand was slid against the meter ruler so that its reading indicated the distance of the probe from the centre if the sphere.
15. Readings of the distance of the probe from the centre of the sphere and the potential measured by the probe were taken. The results were tabulated.

Theories:

The flame probe is made from a plastic hypodermic syringe with the plunger removed. The syringe is fitted into a rubber tubing and is connected to the gas supply. A 2-m wire is hooked to the needle at one end and fixed to the cap of a goldleaf electroscope at the other. The syringe, the rubber tubing and the wire are all fastened with adhesive tape to a perspex rod.

When the flame probe is placed near a positively charge object, negative charges are induced on the needle whilst positive induced charges appear on the leaf of the electroscope. As a result, the leaf deflects.

The small flame from the probe produces positive ions (and also negative ions) which neutralize the negative charges on the needle and so the needle becomes uncharged. The leaf remains positively charged and is at the same potential as the uncharged needle since they are connected.

If the electroscope has been calibrated, the potential can be read from the deflection of the leaf. The flame probe can therefore be used to measure the electric potential at a point in the air.

Measurements:

• Calibrating the electroscope

• When the voltage increases, the deflection of leaf increases proportionally.

• Potential between two parallel plates

• When the flame probe is moved in a plane 0.14m from the earthed metal plates and parallel to it, the deflection of the leaf remains unchanged, the electric potential shown remains 1.5kV.

• When the flame probe is moved across from the earthed plate to the positive plate, the deflection of the leaf increased, the electric potential shown increased from 0 kV to 4.3 kV.

• By E = dV/dr = △V/△r = (4.3-0.4)kV/(0.3-0.02)m = 13.9NC-1

A graph of V against d gives a straight line with positive slope passing through 0. It shows that the electric potential measured by the probe is directly proportional to the distance of the probe from the earthed plate.

• Potential around a charged sphere

• When the flame probe is moved around the sphere, keeping it at a 0.05m from the centre of the sphere, the deflection of the leaf remains unchanged, the electric potential shown remains 3.5kV.

• When the flame probe is moved away, keeping it at the same level as the centre of the sphere, the deflection of the leaf decreased from 3.5kV to 1.1kV.

A graph of V against 1/d gives a straight line with positive slope from x=0.05m. It shows that the electric potential measured by the probe is inversely proportional to the distance of the probe from the surface of the sphere.

Discussion:

• A voltmeter or a CRO cannot be used to measure the electric potential at a point in the air because both instruments draw a small current to produce a deflection and this will disturb the electric field.

• With no flame, the probe may acquire an induced charge and thus affect the field around it, altering the potential at the needle. Therefore, a flame probe is used. It produces positive and negative ions which discharge the needle so that the needle becomes uncharged due to neutralization. Since the needle is now neutralized, its potential is the same as the original potential.

• Sources of error:

When measuring the distance of the probe from the centre of the sphere, a piece of string with a mass attached was dropped from the sphere for locating the zero mark of the meter ruler. This may not be accurate as the sting may not be vertically below the centre of the sphere

• Precautions:

1. The wire which connects the needle and the electroscope cannot touch the bench or any other earthed conductor. This is to prevent charge leakage.
2. The charged sphere must be well away from the walls and the bench top as the induced charges on these objects will upset electric field.

Conclusion:

• Between two parallel plates:

• the electric potential remains constant at constant distance from the metal plates
• the electric potential is proportionally to the distance from the earthed plates

• Around a charged sphere:

• the electric potential remains constant at constant distance from the centre of sphere
• the electric potential is inversely proportionally to the distance from the surface of sphere