To find the magnitude of the force on the test charge, we can use Coulomb's law, which states that the force between two charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.
Let's calculate the force step by step:
1. Calculate the distance between the test charge and the +6μC charge when the test charge is placed halfway between the +6μC and +3μC charges:
The total distance between the +6μC and +3μC charges is 14 cm, so the distance between the test charge and the +6μC charge is half of that, which is 14 cm / 2 = 7 cm = 0.07 m.
1. Calculate the force between the test charge and the +6μC charge:
Using Coulomb's law, the force (F) between two charges (q1 and q2) separated by a distance (r) is given by the formula:
F = (k * |q1 * q2|) / r^2
where:
F is the force,
k is the electrostatic constant (approximately 9 x 10^9 Nm^2/C^2),
q1 and q2 are the charges, and
r is the distance between the charges.
Plugging in the values:
F = (9 x 10^9 Nm^2/C^2) * |(+5μC) * (+6μC)| / (0.07 m)^2
Note that we take the absolute value of the product of the charges since the force is always attractive for opposite charges.
Calculating the force:
F = (9 x 10^9 Nm^2/C^2) * (5 x 10^-6 C * 6 x 10^-6 C) / (0.07 m)^2
F ≈ 1.02 N
Therefore, the magnitude of the force on the test charge is approximately 1.02 N.
To determine the direction of the force, we need to consider the nature of the charges involved. The test charge (+5μC) is positive, while the +6μC charge is also positive. According to Coulomb's law, like charges repel each other, so the force will be directed away from the +6μC charge. Therefore, the direction of the force is away from the +6μC charge.