A particle carring a charge of 6*10^-5C is located half way b/n two charges 40cm apart. One carries a charge of 1*10^-4C and the other -1*10^-4 C. If the three charges lie on the same straight line, what is the magnitude and direction of force on the 6*10^-5 C charge?
Add the Coulomb forces. They will be equal and in the same direction, because the 6*10^-5 C charge is midway between charges of equal magnitude and opposite sign.
To find the magnitude and direction of the force on the 6*10^-5 C 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. The formula for Coulomb's Law is:
F = k * (|q1 * q2|) / r^2
Where:
F is the magnitude of the force,
k is the electrostatic constant (9 × 10^9 N·m^2/C^2),
q1 and q2 are the charges,
|r| is the distance between the charges.
In this case, we have three charges arranged in a straight line: the middle charge is 6*10^-5 C, and the other charges are 1*10^-4 C and -1*10^-4 C, located 40 cm apart.
To find the force on the 6*10^-5 C charge, we need to calculate the forces due to the other two charges and then add them together because the forces are vector quantities.
Let's consider the force due to the positive 1*10^-4 C charge on the 6*10^-5 C charge. Using Coulomb's Law:
F1 = k * |q1 * q2| / r^2
= (9 × 10^9 N·m^2/C^2) * (6*10^-5 C * 1*10^-4 C) / (0.20 m)^2
= (9 × 10^9 N·m^2/C^2) * (6*10^-9 C^2) / 0.04 m^2
= 1.35 N
The force due to the positive charge is 1.35 N, directed towards the positive charge.
Next, let's consider the force due to the negative 1*10^-4 C charge on the 6*10^-5 C charge. Using Coulomb's Law:
F2 = k * |q1 * q2| / r^2
= (9 × 10^9 N·m^2/C^2) * (6*10^-5 C * 1*10^-4 C) / (0.20 m)^2
= (9 × 10^9 N·m^2/C^2) * (6*10^-9 C^2) / 0.04 m^2
= 1.35 N
The force due to the negative charge is also 1.35 N but directed towards the negative charge.
To find the net force, we need to consider the direction of the forces. Since both the forces are equal in magnitude but opposite in direction, they cancel each other out. Therefore, the net force on the 6*10^-5 C charge is zero.
In summary, the magnitude of the force on the 6*10^-5 C charge is zero, and the direction of the force is undetermined due to the cancelation of the forces from the positive and negative charges.