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.

draw the sketch. The two adjacent corners provide 1.414kq/1.48^2

the opposite corner provides kq/(1.414*1.38)^2

add them. Direction is along the extended diagonal.

To calculate the magnitude of the electric field at one corner of the square, we can use Coulomb's Law. Coulomb's Law states that the magnitude of the electric field between two point charges is given by the equation:

E = k * |q| / r^2

Where:
E is the electric field
k is Coulomb's constant (k ≈ 9 × 10^9 Nm^2/C^2)
|q| is the magnitude of the charge
r is the distance between the charges

In this case, the corner of the square is a distance 1.48 m away from the other three corners that are occupied by charges. We have three charges: q1 = q2 = q3 = 1.92 × 10^(-6) C.

To calculate the electric field at the corner, we first calculate the electric field due to each charge separately, and then combine them using vector addition, since all three charges contribute to the electric field at the corner.

Let's calculate the electric field contribution due to one charge:

E1 = k * |q1| / r^2 = (9 × 10^9 Nm^2/C^2) * (1.92 × 10^(-6) C) / (1.48 m)^2

Evaluating this expression:

E1 = (9 × 10^9 Nm^2/C^2) * (1.92 × 10^(-6) C) / (1.48 m)^2 = 21,419 N/C

This gives us the electric field contribution due to one charge. However, since there are three charges, we need to calculate the total electric field at the corner.

Considering that the three charges are located at different corners of the square, we need to calculate the total electric field vector by using vector addition. The electric field is a vector quantity, so it has both magnitude and direction.

To perform vector addition, we consider the net electric field as the result of adding all three electric field vectors together. Since the charges are located at three different corners of the square, we have two electric field vectors pointing towards the corner we are interested in, and one pointing away.

The electric field vectors pointing towards the corner will have a magnitude of 21,419 N/C, which we calculated earlier. The electric field vector pointing away from the corner will have the same magnitude but in the opposite direction.

To calculate the net electric field, we use the Pythagorean theorem. Considering the magnitude of each electric field vector to be 21,419 N/C:

net E = sqrt((21,419 N/C)^2 + (21,419 N/C)^2)

Evaluating this expression:

net E = sqrt((21,419 N/C)^2 + (21,419 N/C)^2) ≈ 30,230 N/C

Therefore, the magnitude of the electric field at one corner of the square, due to the three corner charges, is approximately 30,230 N/C.