The electrical breakdown of an insulator occurs when an electric field becomes l

Question

The electrical breakdown of an insulator occurs when an electric field becomes large enough to ionize the insulator, allowing electrical current to flow; lightning is an example of the electrical breakdown of air. The electrical breakdown of air occurs when the electric field reaches about 3 x 10* N/C. Estimate the magnitude of the total static charge on your body qbody when you generate a static spark with your fingertip when getting out of your car. Assume a spark gap of 1 mm Assume that the static charge on your fingertip is primarily responsible for the electric field you generate near the door right before you touch it. Treat the charge on your fingertip as a point charge. The magnitude of the electric field generated by a point charge is proportional to the magnitude of charge and inversely proportional to the square of thoe distance away from the charge. body 3.34 x10-10 Additionally, assume a uniform static charge density over the surface of your body. A uniform surface charge density ? is calculated by dividing the total charge on the surface Q by the area of the surface A Estimate the percentage that the surface area of one fingertip contributes to your overall body surface area.

Explanation / Answer

Electrical breakdown strength of the air = 3.0 x 10^6 N/C

Given that, spark gap, d = 1 mm = 1 x 10^-3 m

Assume the body as a point charge of Q in magnitude.

So, electric field strength at a distance d is given by -

E = k*Q / d^2 (where k = 9 x 10^9 N*m^2 / C^2)

Put the values -

3 x 10^6 = (9 x 10^9 x Q) / (10^-3)^2

=> 3 x 10^6 x 10^-6 = 9 x 10^9 x Q

=> Q = 3 / (9 x 10^9) = 3.33 x 10^-10 Coulomb.

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