Two charges are placed on the x axis. One of the charges (q1 = +5.44C) is at x1 = +3.00 cm and the other (q2 = -27.7C) is at x2 = +9.00 cm. Find the net electric field (magnitude and direction given as a plus or minus sign) at (a) x = 0 cm and (b) x = +6.00 cm.
To find the net electric field at a certain point, we need to calculate the electric field contribution of each charge at that point.
The magnitude of the electric field due to a point charge can be calculated using Coulomb's Law:
E = k * |q| / r^2
Where:
- E is the electric field magnitude
- k is Coulomb's constant ≈ 9.0 x 10^9 N*m²/C²
- |q| is the magnitude of the charge
- r is the distance between the charge and the point where we want to find the electric field
(a) At x = 0 cm:
To find the net electric field at x = 0 cm, we need to calculate the electric field due to each charge and then add them together.
For charge q1:
The distance between q1 and x = 0 cm is:
r1 = x - x1 = 0 - 3.00 cm = -3.00 cm (negative because x1 is to the right of x = 0 cm)
The electric field due to q1 is:
E1 = k * |q1| / r1^2
For charge q2:
The distance between q2 and x = 0 cm is:
r2 = x - x2 = 0 - 9.00 cm = -9.00 cm
The electric field due to q2 is:
E2 = k * |q2| / r2^2
Then, the net electric field at x = 0 cm is the sum of these two electric fields:
E_net = E1 + E2
(b) At x = 6.0 cm:
We follow similar steps as above, but the distance between each charge and x = 6.0 cm needs to be calculated.
For charge q1:
The distance between q1 and x = 6.0 cm is:
r1 = x1 - x = 3.00 cm - 6.00 cm = -3.00 cm
The electric field due to q1 is:
E1 = k * |q1| / r1^2
For charge q2:
The distance between q2 and x = 6.0 cm is:
r2 = x2 - x = 9.00 cm - 6.00 cm = +3.00 cm
The electric field due to q2 is:
E2 = k * |q2| / r2^2
Then, the net electric field at x = 6.0 cm is the sum of these two electric fields:
E_net = E1 + E2