Question

A tetrahedron has an equilateral triangle base with 25.0-cm-long edges and three equilateral triangle sides. The base is parallel to the ground, and a vertical uniform electric field of strength 260N/C passes upward through the tetrahedron.
What is the electric flux through the base?







What is the electric flux through each of the three sides?

Answer 1

Answer:

-7.03645640575 Nm²/C

2.34548546858 Nm²/C

Explanation:

S = Surface area

Electric flux through the base is given by

$\phi_b=-\int Eds\\\Rightarrow \phi_b=-ES\\\Rightarrow \phi_b=-260\dfrac{\sqrt{3}}{4}0.25^2\\\Rightarrow \phi_b=-7.03645640575\ Nm^2/C$

The electric flux through the base is -7.03645640575 Nm²/C

Inside the tetrahedron there is no charge so total flux will be zero

$\phi_b+3\phi_s=0\\\Rightarrow \phi_s=-\dfrac{\phi_b}{3}\\\Rightarrow \phi_s=-\dfrac{-7.03645640575}{3}\\\Rightarrow \phi_s=2.34548546858\ Nm^2/C$

The electric flux through the sides is 2.34548546858 Nm²/C