Examine the table below as the spearation distance is doubled ow much does the electrostatic forces decrease?
1 20.0 Cm 0.1280N
2 40.0 cm 0.0320N
3 60.0 Cm 0.0142N
4 80.0 CM 0.0080N
5 100.0 CM 0.0051
To determine how much the electrostatic force decreases as the separation distance is doubled, we need to examine the relationship between the force and the distance. In this case, the force is inversely proportional to the square of the distance.
To find the relationship, we can divide the force by the square of the distance for each set of data. Let's calculate the values:
For the first set of data:
Force = 0.1280 N
Distance = (20.0 cm)^2 = 400.0 cm^2
Force/Distance^2 = 0.1280/400.0 = 0.00032 N/cm^2
For the second set of data:
Force = 0.0320 N
Distance = (40.0 cm)^2 = 1600.0 cm^2
Force/Distance^2 = 0.0320/1600.0 = 0.00002 N/cm^2
For the third set of data:
Force = 0.0142 N
Distance = (60.0 cm)^2 = 3600.0 cm^2
Force/Distance^2 = 0.0142/3600.0 = 0.000004 N/cm^2
For the fourth set of data:
Force = 0.0080 N
Distance = (80.0 cm)^2 = 6400.0 cm^2
Force/Distance^2 = 0.0080/6400.0 = 0.00000125 N/cm^2
For the fifth set of data:
Force = 0.0051 N
Distance = (100.0 cm)^2 = 10000.0 cm^2
Force/Distance^2 = 0.0051/10000.0 = 0.00000051 N/cm^2
Now, let's compare the values of Force/Distance^2 for each set of data:
The ratio for the first set of data is 0.00032 N/cm^2.
The ratio for the second set of data is 0.00002 N/cm^2.
The ratio for the third set of data is 0.000004 N/cm^2.
The ratio for the fourth set of data is 0.00000125 N/cm^2.
The ratio for the fifth set of data is 0.00000051 N/cm^2.
As we can see, as the separation distance is doubled, the electrostatic force decreases by approximately a factor of 10. Therefore, we can conclude that the electrostatic force decreases by about 1/10th when the separation distance is doubled.