A +1.3-nC point charge is placed at one corner of a square (1.1 m on a side), and a -3.1-nC charge is placed on the corner diagonally opposite. What is the magnitude of the electric field at either of the other two corners?

what is cosine 45 * ( k*1.3n/1.1^2 -k*3.1n/1.1^2)

To find the magnitude of the electric field at either of the other two corners of the square, we can use the principle of superposition.

The electric field at a point due to a point charge is given by Coulomb's Law:

E = k * q / r^2

Where:
E is the electric field,
k is Coulomb's constant (approximately 9 × 10^9 N m²/C²),
q is the charge, and
r is the distance between the point charge and the point where we want to find the electric field.

Let's consider one of the other corners of the square. The distance between this corner and the positive charge is the same as the distance between the positive charge and the diagonally opposite negative charge. Let's call this distance "d".

The electric field at this corner due to the positive charge is:

E1 = k * q1 / d^2

The electric field at this corner due to the negative charge is:

E2 = k * q2 / d^2

Since both electric fields are in the same direction (towards the corner), we can add them together to find the total electric field at the corner:

E_total = E1 + E2

Plugging in the values:

E_total = k * q1 / d^2 + k * q2 / d^2
E_total = k * (q1 + q2) / d^2

Now we can substitute the given values:

q1 = +1.3 nC = +1.3 × 10^-9 C
q2 = -3.1 nC = -3.1 × 10^-9 C
d = the length of the side of the square = 1.1 m

Substituting these values into the equation:

E_total = (9 × 10^9 N m²/C²) * (1.3 × 10^-9 C - 3.1 × 10^-9 C) / (1.1 m)^2

Now we can calculate the value of E_total.