Three negative point charges lie along a line

[kirby2]

Three negative point charges lie along a line as shown in the figure.

figure: http://tinyurl.com/7xppvc8

Find the magnitude and direction of the electric field this combination of charges produces at point , which lies 6.00 from the charge measured perpendicular to the line connecting the three charges.

ATTEMPT:

i think the magnitude is to the right, away from the -2.00 uC charge. can someone verify this? i am currently trying to find the magnitude, but i will post it when finished.

 

[mathman44]

Electric fields for negative charges tend to point "towards" the negative charge. So I would not agree that the field points to the right at the point P.

To find the total magnitude/direction, find the magnitude of the field produced by each charge at the point P, and use the fact that the direction of ONE field due to ONE negative charge will point directly from the point P to the negative charge.

 

[kirby2]

thank you. my mistake. for the magnitude i got 1.04E7 N/C. i found the x components of E for the charges. I know that there is no net E in the Y direction. then i added those x components up. is this correct? (1.04E7 N/C)

 

[mathman44]

I haven't done the calculation... but that seems fine.

 

[asteriatic]

I would like to clarify that the direction of the electric field is not determined by the charge of the particles, but rather by the direction of the electric force that these charges exert on a positive test charge. In this case, since all three negative charges are on the same side of the point, the electric field will be directed away from them, towards the right.

To find the magnitude of the electric field, we can use Coulomb's Law, which states that the electric force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. In this case, we have three charges, so we need to find the net force exerted by each one and then add them together vectorially.

Let's label the charges as A, B, and C, with A being the leftmost charge and C being the rightmost charge. The distance between A and the point is 6.00 cm, the distance between B and the point is 4.00 cm, and the distance between C and the point is 8.00 cm.

Using Coulomb's Law, we can find the electric force exerted by each charge on a test charge of +1 Coulomb at the point:

F_A = (9 x 10^9 Nm^2/C^2) * (-2.00 x 10^-6 C) * (1.00 C) / (0.06 m)^2 = -3.33 N

F_B = (9 x 10^9 Nm^2/C^2) * (-4.00 x 10^-6 C) * (1.00 C) / (0.04 m)^2 = -22.5 N

F_C = (9 x 10^9 Nm^2/C^2) * (-5.00 x 10^-6 C) * (1.00 C) / (0.08 m)^2 = -5.63 N

The net force will be the vector sum of these three forces, which we can find using the Pythagorean Theorem and the law of cosines:

F_net = sqrt((-3.33)^2 + (-22.5)^2 + (-5.63)^2 + 2*(-3.33)*(-22.5)*cos(135°)) = 24.8 N

Now, to find the magnitude