Four charges are placed at the four corners of a square of side 15 cm.The charges on the upper left and right corners are +3 uC and -6 uC respectively. The charges on the lower left and right corners are -2.4uC and-9 uC respectively. The net force on -6uC charge is ?
To find the net force on the -6 uC charge, we need to calculate the individual forces exerted on it by the other charges.
The formula to calculate the force between two charges is Coulomb's Law:
F = k * (q1 * q2) / r^2
Where:
F is the force between the charges,
k is the electrostatic constant (k = 9 x 10^9 Nm^2/C^2),
q1 and q2 are the magnitudes of the charges, and
r is the distance between the charges.
Let's calculate the individual forces first:
1. Upper left charge (+3 uC) to the -6 uC charge:
The distance between them is the length of the side of the square, which is 15 cm. Converting to meters, it becomes 0.15 m.
Substituting the values into Coulomb's Law:
F1 = (9 x 10^9 Nm^2/C^2) * (3 x 10^-6 C) * (-6 x 10^-6 C) / (0.15 m)^2
2. Lower left charge (-2.4 uC) to the -6 uC charge:
Again, the distance between them is 0.15 m.
Using Coulomb's Law:
F2 = (9 x 10^9 Nm^2/C^2) * (-2.4 x 10^-6 C) * (-6 x 10^-6 C) / (0.15 m)^2
3. Lower right charge (-9 uC) to the -6 uC charge:
The distance remains 0.15 m.
Calculating using Coulomb's Law:
F3 = (9 x 10^9 Nm^2/C^2) * (-9 x 10^-6 C) * (-6 x 10^-6 C) / (0.15 m)^2
Now, to find the net force, we need to add up the individual forces. However, since two charges are negative and two are positive, the direction of the forces is important.
The forces between like charges (positive-positive or negative-negative) repel each other, while opposite charges (positive-negative) attract each other. So, we need to consider the directions.
1. The upper left charge (+3 uC) and the lower left charge (-2.4 uC) will exert forces in the same direction, pushing away from the -6 uC charge.
2. The upper right charge (-6 uC) and the lower right charge (-9 uC) will exert forces in the opposite direction, pulling towards the -6 uC charge.
Now, let's calculate the net force:
Net Force = F1 - F2 + F3
Substituting the values, compute:
Net Force = (F1 + F3) - F2
Take note of the signs while performing the calculations. The resulting net force will have both magnitude and direction.