Points A, B and C are three points found on each edge of an equilateral triangle, which has an
8 cm length on each side. Suppose a charge of +26 µC was at Point A, and a charge of -26µC
at Point B, calculate the net electric field at Point C due to charges A and B.
To calculate the net electric field at point C due to charges A and B, we need to find the electric field due to each charge separately and then add them vectorially.
The electric field at a point due to a point charge is given by Coulomb's law:
Electric field (E) = (k * Q) / r^2
Where:
- k is the electrostatic constant, approximately equal to 9 x 10^9 Nm²/C²
- Q is the charge of the point charge
- r is the distance from the point charge to the point where the electric field is being calculated
First, let's calculate the electric field at point C due to charge A (+26 µC) using Coulomb's law. The distance from A to C is equal to the length of the side of the equilateral triangle, which is 8 cm. Converting it to meters, we have r = 0.08 m.
Using Coulomb's law equation:
Electric field at C due to charge A = (k * Q) / r^2
= (9 x 10^9 Nm²/C² * 26 x 10^-6 C) / (0.08 m)^2
= 2.628 N/C
Now let's calculate the electric field at point C due to charge B (-26 µC) using the same method. The distance from B to C is also equal to 8 cm or 0.08 m.
Electric field at C due to charge B = (k * Q) / r^2
= (9 x 10^9 Nm²/C² * -26 x 10^-6 C) / (0.08 m)^2
= -2.628 N/C
Since electric field is a vector quantity, we need to consider the magnitude and direction.
The net electric field at point C is obtained by adding the electric field vectors at that point due to each charge. The magnitude of the net electric field is the sum of the magnitudes of the individual electric fields. In this case, the magnitudes are equal because both charges have the same magnitude, but opposite signs.
Magnitude of the net electric field at C = |Electric field at C due to charge A| + |Electric field at C due to charge B|
= 2.628 N/C + 2.628 N/C
= 5.256 N/C
The direction of the net electric field can be obtained by considering the direction of the individual electric fields. Since the electric field due to charge A is positive and the electric field due to charge B is negative, they cancel each other out partially. The resulting net electric field at point C will point towards the direction of the stronger electric field (charge A) with a magnitude of 5.256 N/C.