I NEED HELP WITH THIS PHYSICS QUESTION

Question

In the figure below, determine the point (other than infinity) at which the electric field is zero. (Let q1 = -2.40 µC and q2 = 6.20 µC.)

 

_______m

 

 

http://www.webassign.net/serpse8/23-p-021-alt.gif

Answer 1

Hi Porcia!

 

To have the electric field be 0 from two charges, you need two conditions at some point:

 

1.  The electric fields from each charge have equal magnitude

2.  The electric fields from each charge point in opposite directions.

 

The only points on which Condition 2 could be satisfied lie along the line defined by the two point charges (at any point off that line, the directions could never be exactly opposite).  Also, since the charges have opposite sign, the electric fields each one generates in the region between the two charges point in the same direction (away from the positive charge and toward the negative one), and so cannot satisfy Condition 2.

 

Therefore, the only regions in which Condition 2 can be satisfied are along the line defined by the two point charges, either to the left of both or to the right of both.  

 

That takes us to Condition 1.  The magnitudes of the two electric fields at the desired point have to be the same.  Since the greater charge will always have a larger electric field if we go equal distances from both charges, the only way we can have equal magnitudes for both fields at a given point is if we are closer to the smaller charge.  This is analogous to having two light bulbs, with one brighter than the other.  If you want to perceive both bulbs as having equal brightness, you need to hold the dimmer bulb closer to you, with the brighter one farther away, so the greater distance can make it look as dim as the other.  For the same reason, to get equal magnitudes of electric field at a given point from two different magnitude charges, we have to be closer to the smaller charge.

 

Thus, we have to be on the same side of both charges, and closer to the smaller charge.  Now we can calculate how far from the smaller charge we need to be.  We need:

 

kq₁/r² = kq₂/(r + d)²

 

where q₁ is the magnitude of the smaller charge, q₂ is the magnitude of the larger charge, r is the distance of the zero-net-field point from the smaller charge, and d is the distance (presumed known) between the charges.

 

Note that the Coulomb constant cancels out above, leaving you with an equation you can solve for r, if d is known.  Remember to remove the + and - signs from the charges, since those signs have no direct meaning in this expression.

 

I hope this helps!  Let me know if you have any more questions about this, or more information.