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In a rectangular coordinate system, a positive point charge q = 8.50nC is placed at the...

In a rectangular coordinate system, a positive point charge q = 8.50nC is placed at the point x= 0.200m , y=0, and an identical point charge is placed at x= -0.200m , y=0. Find thex and y components and the magnitude and direction of the electric field at the following points. Find the x and y components and the magnitude of the electric field at the origin.

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Answer #1

Charge and their positions:

q1 = 8.5 * 10-9 C          at   x1 = 0.2 m and y = 0 [contributes only to x component of the field]

q2 = 8.5 * 10-9 C          at   x2 = -0.2 m and y = 0 [contributes only to x component of the field]

k = 8.99 * 109 N.m2 / C2 is the Coulomb's force constant

Magnitude and direction of the electric field at the origin:

Electric field due to q1is directed towards the origin since it is positive and electric field due to q2 is directed towards the origin too, as it is positive as well.

X component of the electric field at the origin due to q1 and q2 respectively is,

Ex = k q1 cos 1800 / x12 + k q2 cos 00 / x22

Ex = 8.99 * 109 * 8.5 * 10-9 (-1) / (0.2)2 + 8.99 * 109 * 8.5 * 10-9 (+1) / (0.2)2

Ex = 0 N/C

Since charges are located on the +x-axis and -x-axis, there is no y component of electric field due to these charges. Thus,

Ey = 0 N/C

Thus,

Magnitude of the electric field at the origin due to q1 and q2 E is,

E = ( Ex2 + Ey2 )1/2

E = 0 N/C

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