electric field lines?

Question

suppose two equal and opposite charges are arranged as shown, and that the Q1=Q2=4.0 mico coulombs while the distance between the charges (a)=10cm.

Q1-------------------Q2

consider the point P, located at a distance=5cm directly above Q2

1)draw arrows showing the electric field contributuions of each charge at P.

2) Calculate the net total electric field vector, magnitude and direction at P


im so confused by this question, you dont have to give me the answer just a hint on how to solve..thanks

Answer 1

Since the problem only specifies the charges Q1 and Q2 are opposite, first decide which one is positive charge, and which is negative.

Once you've decided which is positive, you'll have to sketch in arrows that look something like this:
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/imgele/edip2.gif

Remember that electric field lines always start on positive charges, go outward, and eventually wind up on negative charges (or simply going to infinity if there are no negative charges). That means the arrows should point outward from the positive charge, and inward to the negative charge.

For the second question, calculate the distance from each charge to point P separately. Use the electric field equation:
E = 1/(4*pi*e0) * Q/r^2 * r_hat

where e0 is the permittivity of free space (a universal constant, found in your book), Q is the charge (be mindful of the sign), r is the distance from point P to the charge in question, and r_hat is the unit VECTOR that goes from the charge to the point (in that direction, and not the other way around). Remember unit vectors have a magnitude of 1.

Once you know the electric field magnitude and direction (remember it's a vector quantity) due to each particle separate, use vector addition and simply add the vectors.

Answer 2

A "field line" is DEFINED to be a line which connects ALL points in space which have the same potential. A 2nd separate "field line" would connect all points which have the equal potentials (again), but which potential is different from the 1st one. And so on.... Its just a way of visualising a field. Having SAID that .. if 2 such equi-potential lines crossed, then that would mean that AT the point they cross, the field has TWO distinct potential values at the same time. Which is obviously not possible. This is the same concept as the contour lines on a map of a mountain (or a myriad of such diagrams) where each contour line marks all points which are at the same HEIGHT. Obviously no two height lines could cross - because how could a single point on the mountain have 2 different heights ? see ? :)