Problem: Two charged particles, with charges q1 = q and q2 = 4q, are located at a distance d = 2.00cm apart on the x-axis. A third charged particle, with charge q3 = q, is placed on the x-axis such that the magnitude of the force that charge 1 exerts on charge 3 is equal to the force that charge 2 exerts on charge 3. Find the position of charge 3 when q = 2.00 nC.  Assuming charge 1 is located at the origin of the x-axis and the positive x-axis points to the right, find the two possible values, x3,r and x3,l for the position of charge 3.

FREE Expert Solution

Coulomb's law for point charges::

F=kq1q2r2

Quadratic formula:

x=-b±b2-4ac2a

Expansion formular:

(a-b)2=a2-2ab+b2

d = 2.00 cm(1m/100cm) = 0.02 m

Assume the third charge is located between the two charges such that:

r13 = (d - x) m

r23 = x m

q1 = q = 2.00 nC(10-9C/1nC) = 2.00 × 10-9 C

q2 = 4q = 8.00 nC(10-9C/1nC) = 8.00 × 10-9 C

q3 = q = 2.00 nC(10-9C/1nC) = 2.00 × 10-9 C

We are told that F13 = F23:

F13=F23kq1q3(r13)2=kq2q3(r23)22.00×10-9(0.02-x)2=8.00×10-9x22x2=8(x2-0.04x+0.0004)0=8x2-2x2-0.32x+0.0032=6x2-0.32x+0.0032

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Problem Details
Two charged particles, with charges q1 = q and q2 = 4q, are located at a distance d = 2.00cm apart on the x-axis. A third charged particle, with charge q3 = q, is placed on the x-axis such that the magnitude of the force that charge 1 exerts on charge 3 is equal to the force that charge 2 exerts on charge 3. 

Find the position of charge 3 when q = 2.00 nC.  Assuming charge 1 is located at the origin of the x-axis and the positive x-axis points to the right, find the two possible values, x3,r and x3,l for the position of charge 3.