Calculate the magnitude of the electric field at one corner of a square 1.48m on a side if the other three corners are occupied by 1.92×10−6 Ccharges.
To calculate the magnitude of the electric field at one corner of a square, we can use Coulomb's Law, which states that the electric field created by a point charge is given by:
E = k * (q / r^2)
Where:
- E is the magnitude of the electric field.
- k is the electrostatic constant, approximately equal to 9 x 10^9 N m^2/C^2.
- q is the charge.
- r is the distance between the charge and the point where we want to calculate the electric field.
In this case, the three separate point charges at the corners of the square will create an electric field at the corner we are interested in.
Let's assume that the charges at each corner of the square have the same magnitude, q = 1.92 x 10^(-6) C.
To calculate the electric field at the corner, we need to find the distance between the corner and the charges. Since the other three corners of the square form an equilateral triangle, we can use trigonometry to find the distance (r).
The side of the square is given as 1.48 m. We can split the equilateral triangle formed by the three charges into two right-angled triangles.
To find the distance between the corner and one of the charges (r):
1. Draw a line from the corner to the midpoint of one of the sides of the square.
2. This line will divide the equilateral triangle into two congruent right-angled triangles.
3. The height of the right-angled triangle can be found using the Pythagorean theorem: h = (1.48/2) = 0.74 m (half the side of the square).
4. The base of the right-angled triangle can be found using the trigonometric relationship between the base and height: b = h * tan(30°) = 0.74 * tan(30°) = 0.427 m.
5. The distance (r) between the corner and the charge is equal to the hypotenuse of this right-angled triangle: r = √(h^2 + b^2) = √(0.74^2 + 0.427^2) = 0.867 m.
Now that we have the distance (r), we can calculate the electric field (E) at the corner using Coulomb's Law:
E = k * (q / r^2) = (9 x 10^9 N m^2/C^2) * (1.92 x 10^(-6) C / (0.867 m)^2)
Calculating this expression will give you the magnitude of the electric field at one corner of the square.