Question

The Earth produces an inwardly directed electric field of magnitude 150V/m near its surface. (a) What is the potential of the Earth's surface relative to V=0 at r=[infinity]? (b) If the potential of the Earth is chosen to be zero, what is the potential at infinity? (Ignore the fact that positive charge in the ionosphere approximately cancels the Earth's net charge; how would this affect your answer?)

Answer 1

a

The potential of the earth surface is
`V_E= - 9.6*10^9 V`

b

when the potential of the earth is zero the charge is choose to be negative this implies that the potential at infinity would be
`V_\infty=+9.6*10^9V` and (Ignore the fact that positive charge in the ionosphere approximately cancels the Earth's net charge the potential at the surface increase and the electric field remains the same

Step-by-step explanation:

From the question we are told that

The magnitude electric field is
`E = 150V/m`

The potential of the earth surface when V = 0 and
`r = \infty` is mathematically represented as

`V_E = - (q)/(4 \pi \epsilon_o r) = - E *R`

Where q is the charge on the surface of the earth which is negative

R is the radius of the earth

`V_E = 150 * 64 *10^6`

`V_E= - 9.6*10^9 V`

when the potential of the earth is zero the charge is choose to be negative

Then the potential at infinity would be
`+9.6*10^9V`