Three point charges are located away from a dot. charge 1 is 3 cm north of the dot and is 2.1 nC. Charge 2 is 5 cm east of the dot and is -5nC. Charge 3 is -10nC and is located 45 degrees northeast and 5.831 cm away from the dot. What is the net electric field at the position of the dot?
This is simple vector addition using kq/r^2 as the magnitude. The NE charge will need to be split into its components sin 45 and cos45 times the magnitude. And watch your signs, the N and NE have OPPOSITE signs and will act against each other.
To find the net electric field at the position of the dot, we need to calculate the electric fields due to each individual charge and then sum them up as vectors.
Let's start by finding the electric field due to each charge:
1. Charge 1:
- Charge: 2.1 nC
- Distance: 3 cm = 0.03 m (north)
- Electric field due to charge 1 can be calculated using the formula:
E1 = (k * q1) / r^2
where k is the electrostatic constant (9 x 10^9 Nm^2/C^2), q1 is the charge of charge 1 (2.1 nC = 2.1 x 10^-9 C) and r is the distance.
- E1 = (9 x 10^9 Nm^2/C^2) * (2.1 x 10^-9 C) / (0.03 m)^2
2. Charge 2:
- Charge: -5 nC
- Distance: 5 cm = 0.05 m (east)
- Electric field due to charge 2 can be calculated using the same formula as above, with the charge being negative:
E2 = (k * q2) / r^2
where q2 is the charge of charge 2 (-5 nC = -5 x 10^-9 C) and r is the distance.
- E2 = (9 x 10^9 Nm^2/C^2) * (-5 x 10^-9 C) / (0.05 m)^2
3. Charge 3:
- Charge: -10 nC
- Distance: 5.831 cm = 0.05831 m (45 degrees northeast)
- Since the charge is at an angle, we need to find the x-component and y-component of the electric field due to charge 3.
- The x-component can be calculated as Ex = (k * q3 * cos θ) / r^2, where θ is the angle of 45 degrees and r is the distance.
- The y-component can be calculated as Ey = (k * q3 * sin θ) / r^2
- Electric field due to charge 3 can be calculated using the Pythagorean theorem: E3 = sqrt(Ex^2 + Ey^2)
After calculating the electric fields due to each charge, we can sum them up as vectors to find the net electric field at the position of the dot. The net electric field is the vector sum of all the individual electric fields.