Electric Field and point charges problem

[Roshio6969]

A point charge q_1=-4.00\;{\rm nC} is at the point x = 0.600 m, y = 0.800 m, and a second point charge q_2=+6.00\;{\rm nC} is at the point x = 0.600 m, y = 0.

Calculate the magnitude of the net electric field at the origin due to these two point charges.

 

[Pyrrhus]

What have you done? Start setting up the vectors.

 

[quicknote]

The magnitude of the net electric field at the origin due to these two point charges can be calculated using the formula E = kq/r^2, where k is the Coulomb's constant, q is the charge of the point charge, and r is the distance from the point charge to the origin.

For point charge q_1 at (0.600 m, 0.800 m), the distance to the origin is r_1 = √(0.600^2 + 0.800^2) = 1.000 m.

For point charge q_2 at (0.600 m, 0), the distance to the origin is r_2 = √(0.600^2 + 0^2) = 0.600 m.

Substituting the values into the formula, we get:

E_1 = (9.0 x 10^9 Nm^2/C^2)(-4.00 x 10^-9 C)/(1.000 m)^2 = -36.0 N/C

E_2 = (9.0 x 10^9 Nm^2/C^2)(6.00 x 10^-9 C)/(0.600 m)^2 = 150.0 N/C

The net electric field at the origin will be the vector sum of E_1 and E_2, which can be calculated using the Pythagorean theorem:

E_net = √(E_1^2 + E_2^2) = √((-36.0 N/C)^2 + (150.0 N/C)^2) = 156.0 N/C

Therefore, the magnitude of the net electric field at the origin due to these two point charges is 156.0 N/C. This result shows that the electric field at the origin is directed towards the positive charge q_2, as expected since opposite charges attract each other.