Two point charges, 3.4 C and -2.0 C , are placed 5.0 cm apart on the x axis. Ass

Question

Two point charges, 3.4 C and -2.0 C , are placed 5.0 cm apart on the x axis. Assume that the negative charge is at the origin, and the positive x-axis is directed from the negative charge to the positive.

At what points along the x axis is the electric field zero.

Express your answer using two significant figures. If there is more than one answer, give your answers separated by commas.

At what points along the x axis is the potential zero? Let V=0 at r=.

Express your answer using two significant figures. If there is more than one answer, give your answers separated by commas.

Explanation / Answer

let us at a disatnce x from the origin the field is zero

Field due to -2uC is E1 = -k*q1/x^2 = (-9*10^9*2*10^-6)/(x^2)

Field due to 3.4uC is E2 = k*q2/((x-0.05)^2 = (9*10^9*3.4*10^-6)/(x-0.05)^2

then

E1 = E2

(-9*10^9*2*10^-6)/(x^2) = (9*10^9*3.4*10^-6)/(x-0.05)^2

2/x^2 = 3.4/(x-0.05)^2

at x = -0.164 m = -16.4 cm the field is zero

-----------------------------------------------------

Potential due to -2uC is V1= k*q1/x1 = (-9*10^9*2*10^-6)/(x1)

Potential due to 3.4 uC is V2 = k*q2/(0.05-x) = (9*10^9*3.4*10^-6)/(0.05-x1)

then V1 = V2

(-9*10^9*2*10^-6)/(x1) = (9*10^9*3.4*10^-6)/(0.05-x1)

2/x1 = 3.4/(0.05-x1)

x1= 0.0185 m = 1.85 cm

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