As shown in the figure, a square has sides of 8.0 cm with a charge of +6.0 µC at one corner (a) and with charges of -2.0 µC at the remaining three corners (b, c, and d).
The figure is just a square with no measurements. Corner a being the top left corner, corner b top right corner, corner d is bottom left, and corner c is bottom right.
Find the electric field at the center of the square.
___ N/C towards corner C.
I've tried working this problem out a few ways. Like using (8.99e9)(6.0e-6)/8.0cm
&
(8.99e9)(2.0e-6)/8.0cm
I get answers ranging from 5.3e8 N/C to 11.22 N/C.
Any suggestions?
Well, if all the corners had the same charge, the E would be zero. So you are really just dealing with the excess charge: At a, you have a +8microC excess (assuming -2microC starting at each corner). Well, The E will be
E=kQexcess/distance^2
Qexcess is 8microC, distance is the distance from a to the center (8cm*.707)
, of course, distance has to be in meters.
Check my thinking.
Still couldn't get the correct answer :[
To find the electric field at the center of the square, you can consider each charge separately and then add their contributions together. The formula to calculate the electric field due to a point charge is:
Electric Field (E) = (k * q) / r^2
Where:
- k is the electrostatic constant (8.99 x 10^9 Nm^2/C^2)
- q is the magnitude of the charge
- r is the distance between the charge and the point where you want to find the electric field
First, let's calculate the electric field due to the +6.0 µC charge at corner a. The distance from corner a to the center of the square is half the diagonal of the square, which can be found using the Pythagorean theorem.
Using the formula for the diagonal of a square:
diagonal = side * sqrt(2) = 8.0 cm * sqrt(2)
Now, divide the diagonal by 2 to find the distance from corner a to the center:
distance_a = (8.0 cm * sqrt(2)) / 2
Plug these values into the electric field formula for the +6.0 µC charge:
E_a = (8.99 x 10^9 Nm^2/C^2) * (6.0 x 10^-6 C) / (distance_a)^2
Next, calculate the electric field due to each of the -2.0 µC charges at corners b, c, and d. The distance from each corner to the center is the same, which is equal to half the side length of the square:
distance_bcd = 8.0 cm / 2
Plug these values into the electric field formula for the -2.0 µC charges:
E_bcd = (8.99 x 10^9 Nm^2/C^2) * (-2.0 x 10^-6 C) / (distance_bcd)^2
Finally, add the electric fields due to all the charges together since electric fields add as vectors:
E_total = E_a + E_bcd + E_bcd + E_bcd
Now, substitute the values into the formulas, perform the calculations, and add the electric fields together to get the final answer.