The concept of Coulomb’s law is required to solve the problem.
First, use Coulomb’s law and determine the magnitude of the forces on charge due to the charge and charge . Then equate the two forces and determine the magnitude of the charge . Finally, determine the sign of the charge by using the sign of charge and charge .
According to Coulomb’s law, the net force acting on a charge due to another charge Q is directly proportional to the product of the two charges and inversely proportional to the square of the distance between them. The expression for the magnitude of the electric force acting on the charge q is given as,
Here, k is the Coulomb’s constant and r is the distance between the two charges.
The magnitude of the force acting on charge due to the charge is given as,
Here, is the distance between the charges and .
The magnitude of the force acting on charge due to the charge is given as,
Here, is the distance between the charges and .
The net force acting on the charge is zero if the magnitude of the force acting on the charge due to the charge is equal to the magnitude of the force due to the charge . That is,
Substitute for and for in the equation and solve for .
Substitute for , 2.00 cm for , and 4.00 cm for in the equation .
The following figure shows the direction of the forces acting on the charge .
The charge is positive and charge is negative. Therefore, the force between the charges and is attractive and the direction of the force on charge due to the charge is towards right.
The net force acting on the charge is zero if the force acting on the charge due to the charge is equal and opposite to the force due to the charge . Therefore, the direction of the force on charge due to the charge is towards left. This implies that the force between the charges and is repulsive.
The force between the charges and is repulsive if both the charges and are of same sign. Hence, the sign of the charge is positive.
Ans:The magnitude of the charge is and it is of positive sign.
Three point charges are arranged on a line. Charge q3=+5.00x10^-9C and is at the origin. Charge q2=-3.00x10^-9C and is a...
Three point charges are arranged on a line. Charge q3 = +5.00nC and is at the origin. Charge q2 = -3.50 nC and is at x = 5.00 cm . Charge q1 is at x = 1.50 cm . What is q1 (magnitude and sign) if the net force on q3 is zero?
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Three point charges are arranged on a line. Charge q3 = +5.00 nC and is at the origin. Charge q2 = -2.00 nC and is at x = 3.50 cm . Charge q1 is at x = 1.50 cm . What is q1 (magnitude and sign) if the net force on q3 is zero?
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