A point charge of -14nC and +12nC is located 12cm along the x-axis. Determine the magnitude and direction of the electric field intensity at point P at the mid-point and 8cm perpendicular from the x-axis:
p
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| 8.0cm
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|
-14nC.---------------. 12 nC
6cm 6cm
Please help getting mixed up with the theory! Thanks!!!!
Sorry the diagram didn't come out right!
To determine the magnitude and direction of the electric field intensity at point P, you can use the principle of superposition. This principle states that the electric field at a point due to multiple charges is the vector sum of the electric fields produced by each individual charge.
Step 1: Calculate the electric field intensity due to the -14nC charge at point P.
- The formula to calculate the electric field intensity is given by:
E = k * (q / r^2)
Where:
E is the magnitude of the electric field intensity,
k is the electrostatic constant (k = 9 × 10^9 Nm^2/C^2),
q is the charge of the point charge, and
r is the distance from the point charge to the point where you want to calculate the electric field intensity.
- In this case, the distance from the -14nC charge to point P is 6cm. So, r = 6cm = 0.06m.
- Plugging the values into the formula:
E1 = (9 × 10^9 Nm^2/C^2) * (-14nC) / (0.06m)^2
Step 2: Calculate the electric field intensity due to the +12nC charge at point P.
- The distance from the +12nC charge to point P is also 6cm (0.06m).
- Plugging the values into the formula:
E2 = (9 × 10^9 Nm^2/C^2) * (12nC) / (0.06m)^2
Step 3: Calculate the net electric field intensity at point P.
- The principle of superposition states that the net electric field intensity is the vector sum of the individual electric field intensities.
- Since the charges are opposite in sign, the electric field intensity due to the -14nC charge will be in the opposite direction to that due to the +12nC charge.
- Subtract the magnitudes of E1 and E2 to find the net electric field intensity:
E_net = |E1| - |E2|
Step 4: Determine the direction of the electric field intensity at point P.
- The direction can be determined by considering the sign of the net electric field intensity.
- If E_net is positive, the electric field intensity points away from the charges (outward).
- If E_net is negative, the electric field intensity points towards the charges (inward).
So, by following these steps, you can calculate the magnitude and direction of the electric field intensity at point P.