charges of -6nC and 4nC are 3m apart.(a)Determine the force they exert on each other.(b) the net electric field intensity at a point midway between them.
To determine the force between the charges, you can use Coulomb's Law. Coulomb's Law states that the force between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
(a) To determine the force between the charges of -6nC and 4nC, follow these steps:
1. Identify the given quantities:
- Charge 1 (q1) = -6nC
- Charge 2 (q2) = 4nC
- Distance between the charges (r) = 3m
2. Convert the charges to coulombs (C):
- Charge 1 (q1) = -6nC = -6 * 10^-9 C
- Charge 2 (q2) = 4nC = 4 * 10^-9 C
3. Use Coulomb's Law formula to calculate the force (F):
F = k * (|q1| * |q2|) / r^2
where k is the electrostatic constant, which is approximately equal to 9 × 10^9 N m²/C².
Plugging in the values:
F = (9 * 10^9 N m²/C²) * ((|-6 * 10^-9 C|) * (|4 * 10^-9 C|)) / (3m)^2
4. Calculate the force:
F = (9 * 10^9 N m²/C²) * (6 * 10^-9 C) * (4 * 10^-9 C) / 9m²
F = (9 * 6 * 4) * 10^-9 / 9m²
F = 24 * 10^-9 / 9m²
F = 2.67 * 10^-9 N (approximately)
Therefore, the force exerted between the charges is approximately 2.67 * 10^-9 N.
(b) To determine the net electric field intensity at a point midway between the charges, follow these steps:
1. The electric field intensity (E) created by a point charge is given by the equation:
E = k * (q/r^2)
where k is the electrostatic constant, q is the charge, and r is the distance from the charge.
2. Calculate the electric fields created by each charge at the point midway between them:
- For charge q1:
E1 = (9 * 10^9 N m²/C²) * (|-6 * 10^-9 C|) / (1.5m)^2
- For charge q2:
E2 = (9 * 10^9 N m²/C²) * (|4 * 10^-9 C|) / (1.5m)^2
3. Calculate the net electric field intensity at the midpoint by adding the magnitudes of the individual electric fields and considering their directions. Since the charges have opposite signs, they produce electric fields in opposite directions:
Net E = |E1 - E2|
4. Calculate the net electric field intensity:
Net E = |E1 - E2| = |(9 * 10^9 N m²/C²) * (6 * 10^-9 C) / (1.5m)^2 + (9 * 10^9 N m²/C²) * (4 * 10^-9 C) / (1.5m)^2|
Net E = (9 * 6 + 9 * 4) * 10^-9 / (1.5m)^2
Net E = 90 * 10^-9 / (1.5m)^2
Net E = 60 * 10^-9 / (1.5)²
Net E = 60 * 10^-9 / 2.25
Net E = 26.67 * 10^-9 N/C (approximately)
Therefore, the net electric field intensity at the point midway between the charges is approximately 26.67 * 10^-9 N/C.