What Charge Causes a Pea to Discharge in Dry Air?

[Jodi]

Hi; Could somebody please help me with the following question: Dry air will break down and generate a spark if the electric field exceeds about 2.90E+6 N/C. How much charge could be packed onto a green pea (diameter 0.800 cm) before the pea spontaneously discharges?
The formula i used was E=kq/r^2. And the answer i got was 5.0E-9 C. But that answer is not correct, does anyone know what I am doing wrong? Thanks.

 

[OlderDan]

Hi; Could somebody please help me with the following question: Dry air will break down and generate a spark if the electric field exceeds about 2.90E+6 N/C. How much charge could be packed onto a green pea (diameter 0.800 cm) before the pea spontaneously discharges?
The formula i used was E=kq/r^2. And the answer i got was 5.0E-9 C. But that answer is not correct, does anyone know what I am doing wrong? Thanks.

Check your math and your units. You are doing the right thing.

 

[thepatientmental]

Hi there,

Based on the information provided, it is not entirely clear what formula you used to calculate the charge on the green pea. However, I can offer some clarification and a potential solution.

Firstly, the formula you mentioned, E=kq/r^2, is correct for calculating the electric field strength at a given distance from a point charge. However, this formula does not directly relate to the question at hand, which asks about the charge that can be packed onto the green pea before it discharges.

To answer this question, we can use the concept of electric breakdown voltage. This is the minimum electric field strength required for a material to break down and conduct electricity. In the case of dry air, this breakdown voltage is approximately 2.90E+6 N/C, as stated in the question.

Now, the question asks for the maximum charge that can be packed onto a green pea before it discharges. In other words, we need to find the maximum charge that can be packed onto the pea while keeping the electric field strength below the breakdown voltage of 2.90E+6 N/C.

To do this, we can rearrange the formula for electric field strength to solve for charge, giving us q = Er^2/k. Plugging in the values given in the question (E = 2.90E+6 N/C, r = 0.800 cm, and k = 8.99E+9 Nm^2/C^2), we get q = (2.90E+6 N/C)(0.008 m)^2 / (8.99E+9 Nm^2/C^2) = 2.57E-11 C.

This means that the maximum charge that can be packed onto the green pea without causing it to spontaneously discharge is 2.57E-11 C. This is significantly smaller than the answer you obtained, which suggests that your calculation may have been incorrect. I would recommend double-checking your calculations and units to ensure accuracy.

I hope this helps! Let me know if you have any further questions.