The figure below shows a system consisting of three charges, q 1 = +4.06 µC, q 2

Question

The figure below shows a system consisting of three charges, q1 = +4.06 µC, q2 = +4.06 µC, and q3 = -4.06µC, at the vertices of an equilateral triangle of side d = 2.71cm.

(a) Find the magnitude of the electric field at a point halfway between the charges q1 and q2.
N/C

(b) Is the magnitude of the electric field halfway between the charges q2 and q3 greater than, less than, or the same as the electric field found in part (a)?

greater than? less than? the same?

(c) Find the magnitude of the electric field at the point specified in part (b).
N/C

Explanation / Answer

a) distance from q3 to halfway between the charges q1 and q2,

x = sqrt(d^2 - (d/2)^2)

= sqrt(0.0271^2 - (0.0271/2)^2)

= 0.02347 m

at this point q1 and q2 produce equal and oppsite electric fields.

so,

net electric field, Enet = E3

= k*q3/x^2

= 9*10^9*4.06*10^-6/0.02347^2

= 6.63*10^7 N/C

b) greater than

c) at a point half way between q2 and q3,

E23 = E2 + E3

= k*q2/(d/2)^2 + k*q3/(d/2)^2

= 9*10^9*4.06*10^-6/(0.0271/2)^2 + 9*10^9*4.06*10^-6/(0.0271/2)^2

= 3.98*10^8 N/c

E1 = k*q1/x^2

= 9*10^9*4.06*10^-6/0.02347^2

= 6.63*10^7 N/C

Enet = sqrt(E1^2 + E2^2)

= sqrt(0.663^2 + 3.98^2)*10^8

= 4.03*10^8 N/c

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