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## Homework Statement

Consider 2 charges located in the x-y plane; q

_{1}of magnitude 5 mC (millicoulombs) is located at the origin, and q

_{2}of unknown magnitude is located at (x,y) = (0.1, 0) (in metres). The electric field E at position (0.03, 0.05) is found to be entirely in the +y direction (i.e. the x-component is zero). Determine the sign of charge q

_{1}and the magnitude and sign of charge q

_{2}.

## Homework Equations

|q| = 5mC (microCoulombs)

F= qE ; q= charge, E= electric Field

E(r) = ƩE

_{i}(r)

=1/(4*pi*ε

_{°})*Ʃ(r-r

_{i})*q

_{i}/(r-r

_{i})

^{3}

## The Attempt at a Solution

E

_{1}(for one charge)= 1/(4*pi*ε

_{°})*q

_{1}/r

^{2}

= 1/(4*pi*ε

_{°})* (0.000005 C)/0.0015m

E= 2.996*10

^{7}

Then I went and did,

E=1/(4*pi*ε

_{°})[(q

_{1}/r

^{2})+q

_{2}/(r-r

_{2})

^{2}]

rearrange for q

_{2}and,

q

_{2}= [E(4*pi*ε

_{°})+(r

^{2}/q

_{1})](r-r

_{2})

^{2}

q

_{2}= -29.9997 C. (This seems way to high to be correct)

So q

_{1}is positive to make E in the + y direction.

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