Two tractortrailer trucks are driving sidebyside on intersta

Two tractor-trailer trucks are driving side-by-side on interstate 40. The one on the left hugs the right side of the lane, and the one on the right hugs the left side of the lane, so that the two are almost touching. A physics student driving behind witnesses the event, and realizes that the time is ripe for a daring experiment. With the alacrity of the lone Ranger, he leaps from his car onto the bark of one of the trucks, and climbs on the roof. The student has in his left pocket a 1.5 Volt Eveready battery, and in his right pocket he carries two wires. The battery has a Capacity of 565 mAh. He connects the negative terminal of the buttery to one truck, and the positive terminal to the other in order to charge the trucks, (a) If tin- distance between the trucks is 20 nm, estimate how much charge will be on each of the trucks when equilibrium is reached. (b) How closely the trucks would have to be for the experiment to completely drain the battery, (c) For a separation of 20 nm, what is the strength of the electric field m the gap between the trucks? Does it exceed the dielectric strength of dry air? What is the diameter of an air molecule, by the way?

Solution

a)

Charge on each trucks = 565 mAh

= 565*10^-3*3600

= 2034 C

b)

For draining the battery,

Electric field must be equal to, E = 3*10^6 V/m

So, d = V/E = 1.5/(3*10^6)

= 5*10^-7 m

= 500 nm

c)

for d = 20 nm

E = V/d = 1.5/(20*10^-9)

= 7.5*10^7 V/m <-------answer

So, it exceeds the dielectric strength of dry air

diameter of an air molecule = 4*10^-10 m