two charges +1.2*10^-8 C and -1.6*10^-8 C are placed at the corners A and B of a right angled triangle ABC in which AB=3cm, AC=5cm. find the electric field at C.

YOu know the distances, the E are at right angles, so the E is just a vector combination of the two.

To find the electric field at point C, due to the charges at A and B, we can use the principle of superposition. This principle states that the total electric field at a point is the vector sum of the electric fields created by individual charges.

Let's calculate the electric field at point C due to the charge at A and the charge at B separately, and then add them to get the total electric field at C.

1. Electric field at point C due to the charge at A (E₁):
The magnitude of the electric field at point C due to the charge at A can be calculated using Coulomb's Law:

E₁ = k * (|q₁| / r₁²)

where:
- k is the electrostatic constant, approximately 9 * 10^9 Nm²/C²
- |q₁| is the magnitude of the charge at A, which is 1.2 * 10^-8 C
- r₁ is the distance between charge A and point C, which is AC = 5 cm = 0.05 m

Plug the values into the formula:

E₁ = (9 * 10^9 Nm²/C²) * (1.2 * 10^-8 C / (0.05 m)²)
= (9 * 1.2 * 10^1 * 10^9 * 10^-8) N / 0.05²
= (108 * 10² * 10^-8) N / 0.0025
= (108 * 10^-6) N / 0.0025
= 4.32 N / 0.0025
= 1728 N/C

Since the charge at A is positive, the electric field vector due to this charge points away from A.

2. Electric field at point C due to the charge at B (E₂):
Similarly, calculate the magnitude of the electric field at point C due to the charge at B:

E₂ = k * (|q₂| / r₂²)

where:
- |q₂| is the magnitude of the charge at B, which is 1.6 * 10^-8 C
- r₂ is the distance between charge B and point C, which is BC = 3 cm = 0.03 m

Plug the values into the formula:

E₂ = (9 * 10^9 Nm²/C²) * (1.6 * 10^-8 C / (0.03 m)²)
= (9 * 1.6 * 10^1 * 10^9 * 10^-8) N / 0.03²
= (144 * 10² * 10^-8) N / 0.0009
= (144 * 10^-6) N / 0.0009
= 14.4 N / 0.0009
= 16000 N/C

And since the charge at B is negative, the electric field vector due to this charge points towards B.

3. Total electric field at point C (E_total):
To find the total electric field at point C, we need to add the electric field vectors due to the charges at A and B. However, we need to consider the directions of the electric field vectors.

Since the electric field vector due to the charge at B points towards B and the electric field vector due to the charge at A points away from A, we need to subtract their magnitudes.

E_total = E₁ - E₂
= 1728 N/C - 16000 N/C
= -14272 N/C

The total electric field at point C is -14272 N/C, directed towards B.

To find the electric field at point C, we need to calculate the electric field contribution from each charge separately and then combine them vectorially.

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

E = k * (q / r^2)

Where:
- E is the electric field strength
- k is the electrostatic constant (approximated as 9 × 10^9 N m^2/C^2)
- q is the charge
- r is the distance between the point charge and the location where the electric field is being measured

Let's calculate the electric field contribution from the first charge (+1.2 × 10^-8 C) at point C:

q1 = 1.2 × 10^-8 C (charge at A)
r1 = distance between A and C

Using Pythagoras' theorem, we can find r1:

r1 = √(AC^2 + BC^2)
r1 = √(5cm)^2 + (3cm)^2)
r1 = √(25cm^2 + 9cm^2)
r1 = √(34cm^2)
r1 ≈ 5.83 cm

Now we can calculate the electric field due to the first charge at point C:

E1 = k * (q1 / r1^2)
E1 = (9 × 10^9 N m^2/C^2) * (1.2 × 10^-8 C / (5.83 cm)^2)

Similarly, let's calculate the electric field contribution from the second charge (-1.6 × 10^-8 C) at point C:

q2 = -1.6 × 10^-8 C (charge at B)
r2 = distance between B and C

Using Pythagoras' theorem again, we can find r2:

r2 = √(AC^2 + AB^2)
r2 = √(5cm)^2 + (3cm)^2)
r2 = √(25cm^2 + 9cm^2)
r2 = √(34cm^2)
r2 ≈ 5.83 cm

Now we can calculate the electric field due to the second charge at point C:

E2 = k * (q2 / r2^2)
E2 = (9 × 10^9 N m^2/C^2) * (-1.6 × 10^-8 C / (5.83 cm)^2)

Finally, to get the total electric field at point C, we need to combine the electric field contributions from both charges vectorially:

E_total = E1 + E2

By substituting the values in the above equations, you can find the electric field at point C.