A 3.0-μC positive point charge is located at the origin and a 2.0-μC positive point charge is located at x = 0.00 m, y = 1.0 m. Find the coordinates of the point where the net electric field strength due to these charges is zero.
A) x = 0.00 m, y = 0.55 m
B) x = 0.00 m, y = 0.67 m
C) x = 0.00 m, y = 1.5 m
D) x = 0.00 m, y = 0.60 m

Question

Quizplus · Accepted Answer

The net electric field strength is zero at the point where the electric field strength due to the 3.0-μC charge is equal and opposite to the electric field strength due to the 2.0-μC charge. The electric field strength due to a point charge is given by:$$E = k\frac{q}{r^2}$$where k is Coulomb's constant, q is the charge, and r is the distance from the charge.The electric field strength due to the 3.0-μC charge at the point (x, y) is:$$E_1 = k\frac{3.0\mu C}{(x^2 + y^2)}$$The electric field strength due to the 2.0-μC charge at the point (x, y) is:$$E_2 = k\frac{2.0\mu C}{[(x - 0.00 m)^2 + (y - 1.0 m)^2]}$$The net electric field strength is zero when:$$E_1 = E_2$$$$k\frac{3.0\mu C}{(x^2 + y^2)} = k\frac{2.0\mu C}{[(x - 0.00 m)^2 + (y - 1.0 m)^2]}$$$$\frac{3.0}{(x^2 + y^2)} = \frac{2.0}{[(x - 0.00 m)^2 + (y - 1.0 m)^2]}$$$$3.0[(x - 0.00 m)^2 + (y - 1.0 m)^2] = 2.0(x^2 + y^2)$$$$3.0x^2 - 6.0x + 3.0y^2 - 6.0y + 3.0 = 2.0x^2 + 2.0y^2$$$$x^2 - 6.0x + y^2 - 6.0y + 1.0 = 0$$$$(x - 3.0)^2 + (y - 3.0)^2 = 8.0$$The point where the net electric field strength is zero is at (3.0 m, 3.0 m).

A 30-μC Positive Point Charge Is Located at the Origin and and a 2.0-μC