Question

Figure P15.30 shows the electric field lines for two point charges separated by a small distance. Determine the ratio q_1/q_2. What are the signs of q_1 and q_2? Sketch the electric field lines around an isolated point charge q > 0. Sketch the electric field pattern around an isolated
Problem 30 only

Answer 1

(30) a. The number of lines crossing a surface which is proportional to the electric flux through that surface.

$\Phi$ = $\alpha$ N

We can find the ratio of electric flux through two surfaces by dividing the numbers of lines crossing the surfaces.

Then, we have

_$\Phi$1 / _$\Phi$2 = $\alpha$ N₁ / $\alpha$ N₂

_$\Phi$1 / _$\Phi$2 = N₁ / N₂

From gauss law, the electric flux through a gaussian surface is proportional to the net charge enclosed by the surface. Therefore, the ratio of q₁ / q₂ will be given as :

q₁ / q₂ = - $\varepsilon$_0$\Phi$1 / $\varepsilon$_0$\Phi$2

q₁ / q₂ = - N₁ / N₂

q₁ / q₂ = - (6 / 18)

q₁ / q₂ = - 1 / 3

b. The direction of an electric field lines at each point coincides with the direction of an electric field vector. Therefore, they originate on a positive charge & terminate on negative charge.

The signs of charge q₁ will be negative while a charge q₂ will be positive.