Question

Hey guys! I'm new here and I need some help with an exercise about electricity (electrostatics). I've tried to solve it but I can't figure out how to do it... I'm going to translate the exercise because I have it in Spanish, hehe... Thanks a lot. :)

Two point charges, 5 μC and -10 μC, are 1 m apart. Where, in the line joining the two charges, the electric field is equal to zero?

Answer 1

How could I know where the electric field is going to be?

Answer 2

What have you tried?

Answer 3

Well, one obvious fact is that if the electric field is zero, the net force on any charge at that point must be zero, too. So where, on the line joining these two charges, would the net force on a test charge be equal to zero?

Answer 4

Well, what happens at the point where the electric field is equal to zero? There's no force, right, because F=qE. So, we can rephrase this as, where is the force in equilibrium?

Answer 5

\[ E \prop \frac{q}{r^2} \]
\[ E = 0 = \frac{ 5 }{ \left( x - 0 \right) ^2 } + \frac{ -10 }{ \left( x - 1 \right) ^2 } \]
\[ \left( x - 1 \right) ^2 = 2 x ^2 \Rightarrow x^2 -2x + 1 = 2 x^2 \Rightarrow x^2 + 2x -1 = 0 \Rightarrow x = -1 \pm \sqrt{8} \]

Answer 6

field will can be zero on either side of 5microC or -10 microC,but not in between them...