Dipole question, Quiz this afternoon

[rbraunberger]

Homework Statement

A 5mC charge is glued down at position ( 1m, 2m ). A -3mC charge is glued down at position ( -3m, -6m ). What are the components of the electric field at the point ( 7m, -6m )? If the component points in the negative direction, put in a negative number for your answer.

Homework Equations

E = (kQ)/r^2
E total = sqr ( E1^2 + E2^2 )

The Attempt at a Solution

E1= (8.99e9)(5e-3)/100 = 4.50e5 N/C
E2 = (8.99e9)(-3e-3)/100 = -2.70e5 N/C
E total = 5.25e5

Theta = tan^-1 (E1/E2) = -59

E total * sin (-59) = -4.50e5 = y
E total * cos (-59) = 2.70e5 = x

I worked to this point and have the answers wrong. What am I doing wrong?

 

[anathema]

First, let's clarify the given information. The 5mC and -3mC charges are located at (1m, 2m) and (-3m, -6m) respectively.

To find the electric field at point (7m, -6m), we need to consider the electric fields produced by both charges. The electric field at a point due to a point charge is given by the equation E = (kQ)/r^2, where k is the Coulomb's constant (8.99e9 Nm^2/C^2), Q is the charge, and r is the distance between the point charge and the point where the electric field is being measured.

For the 5mC charge at (1m, 2m), the distance to point (7m, -6m) is r1 = sqrt[(7-1)^2 + (-6-2)^2] = 8.06m. Therefore, the electric field at point (7m, -6m) due to the 5mC charge is E1 = (8.99e9)(5e-6)/8.06^2 = 0.07e5 N/C (note that the charge is in Coulombs, not milliCoulombs).

For the -3mC charge at (-3m, -6m), the distance to point (7m, -6m) is r2 = sqrt[(7+3)^2 + (-6+6)^2] = 10m. Therefore, the electric field at point (7m, -6m) due to the -3mC charge is E2 = (8.99e9)(-3e-6)/10^2 = -0.03e5 N/C.

To find the total electric field at point (7m, -6m), we need to add the vector components of E1 and E2. The x-component of the electric field is given by Ex = E1*cos(theta1) + E2*cos(theta2), where theta1 and theta2 are the angles between the x-axis and the direction of the electric fields E1 and E2 respectively. Similarly, the y-component of the electric field is given by Ey = E1*sin(theta1) + E2*sin(theta2).

To find the angles theta1 and theta2, we can use trigonometry. For