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# Electric forces, field and potentials

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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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This job embodies electric forces, field and potentials.

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A) According to Superposition law, the electric field due to some distribution of charges is equal to the sum of electric fields due to each of those charges. Taking that into account, we just have to find the field due to each of those q0 charges at position (x,y) and sum them to get the total electric field at (x,y). Electric field is a vector value, so we can write:

Etotal = E1 + E2,

Where E1 and E2 are fields due to charges at x=-a and x =a respectively. The E's are vector values.

Now we can write that vector equation in components on x and y axis:

Etotal x = E1 x + E2 x
Etotal y = E1 y + E2 y

B) We can use the ...

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