The Earth possesses an electric field of (average) magnitude near its surface. The field points radially inward. Calculate the net electric flux outward through a spherical surface surrounding, and just beyond, the Earth’s surface.

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The Earth possesses an electric field of (average) magnitude 150 near its surface. The field points radially inward. Calculate the net electric flux outward through a spherical surface surrounding, and just beyond, the Earth's surface.

Explanation:

Given that,

Electric field is 150N/C inward

i.e E = - 150 i

Then, electric flux (Φ) is given as

Φ=∮E.dA

Surface area of a sphere is

A=4πr²

dA=8πr dr

The area is outwardly i.e

dA=-8πr dr i

Φ=∮E.dA

Φ=∮-150 i • 8πr i dr from 0 to R

Φ= -1200π∮rdr. From 0 to R

Φ= -1200π r²/2. From 0 to R

Φ= -600π [R² -0²]

Φ= -600πR²

Where R is radius of earth which is 6,400,000m

Φ= -600πR²

Φ= -600π(6400000)²

Φ= -7.72×10^16 Nm²/C

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