How do you solve these problems? 1.) You construct a parallel plate capacitor wi

Question

How do you solve these problems?

1.) You construct a parallel plate capacitor with a plate spacing of 1.40 cm and a capacitance of 5.30 F. A friend of yours doubles the spacing between the plates and puts a dielectric between them. This changes the capacitance to 14.5 F. What is the dielectric constant of the inserted material?

2.) You've set up an electric field that points along the x-axis (the horizontal direction). The x-component of the field is 2.5x2 in N/C. You want to compute the potential difference between the points (0,0,0) m and (7.3,0,0) m.

3a.) A heavy summer rain has just spoiled a fun game of frisbee between you and your friends. As you rush to leave, a bolt of lightning strikes a tree on the other side of the field. Lightning is a form of electrical discharge that occurs when the electric field in a region between the ground and the clouds ionizes the air. You happen to know that a bolt of lightning can unleash between a hundred-million and a billion joules of energy, transferring tens of coulombs of charge between the earth and the sky. Out of curiosity, you decide to estimate the magnitude of the associated voltage difference.

3b.) You estimate that the lightning travelled along a vertical distance of about a mile. You decide to estimate the magnitude of the average electric field strength across this distance.

Explanation / Answer

there are multiple questions here. They are unrelated. I am allowed to answer only 1 at a time

1)

Cinitial = ebsoleneo*A/d ....eqn 1
C(final) = K*ebsoleneo*A/2d ..eqn 2

divide eqn 2 by eqn 1
C(final) / Cinitial)= (K*ebsoleneo*A/2d)/(ebsoleneo*A/d )
C(final) / C(initial) = K/2
14.5/5.3=K/2
K= 5.47
Answer: dielectric constant of the inserted material is 5.47

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