# Working with electric forces, field and potentials.

Two positive charges, charge q0 are fixed on the x axis at positions +a and -a.

a) What is the Electric Field anywhere in the (x,y) plane, at position (x,y)? Be sure your answer clearly denotes the vector nature of the electric field.

b) What is the electric potential at position (x,y)?

c) A third charge, q3 , (mass m3 ) is at position (0, 0 y ). What is the force on this charge?

d) What is the minimum speed of the third particle at position (0, 0 y ) in order for it to
(i) reach the origin , (0,0)
(ii) move off to infinity (plus or minus).

Be sure to consider both signs of 3 q to answer these.
The answers may not algebraically reduce to 'nice' solutions in general. Be sure to present in terms of defined variables.

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#### Solution Preview

...me superposition law for the electric potential, only it is going to be much easier since electric potentials a scalar value.
So:
Utotal = U1 + U2
Where U1 and U2 are potentials due to charges at x=-1 and x=a respectively.

Now let's write down these potentials for both charges:

U1 = k*q0/[(x+a)2 + y2]1/2 ,
U2 = k*q0/[(x-a)2 + y2]1/2 ,

C) We know that F = q * E, where E is the electric field at the position of charge q, and F is the force on the charge due to that electric field. So all we have to do now is substitute x=0 and y=y in our equations for E from part A) and we will get the force.

D) Here, the answer strongly depends on the sign of q3. If q3>0, then the force F is ...