Charge A has a charge of +2 C. Charge B has a charge of - 3 C and is located 1 meter to the right of A. Charge C is located 1 m to the right of charge Band has a charge of -1C. If a fourth charge (Charge D) is placed 4 m to the right of Charge B, How much charge must it havefor the net force on Charge B to be zero?
To calculate the charge required for Charge D to create a net force of zero on Charge B, we need to consider Coulomb's law, which 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.
Let's break down the problem step by step:
1. Determine the magnitude of the electrostatic force between Charge A and Charge B. We can use Coulomb's law:
FAB = (k * |QA| * |QB|) / rAB²
where FAB is the force between A and B, k is the Coulomb's constant (9 x 10^9 N m²/C²), |QA| is the magnitude of charge A, |QB| is the magnitude of charge B, and rAB is the distance between A and B.
Plugging in the given values:
FAB = (9 x 10^9 N m²/C²) * (2 C) * (3 C) / (1 m)²
= 54 x 10^9 N
2. Calculate the magnitude of the electrostatic force between Charge B and Charge C. Using Coulomb's law:
FBC = (k * |QB| * |QC|) / rBC²
Plugging in the given values:
FBC = (9 x 10^9 N m²/C²) * (3 C) * (1 C) / (1 m)²
= 27 x 10^9 N
3. Determine the net force on Charge B due to Charges A and C. Since the forces are acting in opposite directions, we need to consider their signs:
Net Force on B = FAB - FBC
= 54 x 10^9 N - (-27 x 10^9 N)
= 81 x 10^9 N
The net force on Charge B is 81 x 10^9 N to the left.
4. To cancel out this net force and make it zero, Charge D must exert a force on Charge B equal in magnitude and opposite in direction to the net force. Therefore, it needs to have a charge that would create a force equal to 81 x 10^9 N, with a distance of 4 meters between them.
Let's call the magnitude of Charge D |QD|. Using Coulomb's law once again:
FBD = (k * |QB| * |QD|) / rBD²
Since we want FBD to be 81 x 10^9 N, we can plug in the values and solve for |QD|:
81 x 10^9 N = (9 x 10^9 N m²/C²) * (3 C) * |QD| / (4 m)²
Simplifying the equation and solving for |QD|:
|QD| = (81 x 10^9 N * (4 m)²) / (9 x 10^9 N m²/C² * 3 C)
= 144 C
Therefore, Charge D must have a magnitude of 144 C in order to create a net force of zero on Charge B.
Note: The direction of the charge (positive or negative) is not explicitly mentioned in the problem. These calculations only consider the magnitudes of the charges to determine the net force.
does not matter what the charge on B is, call it -1 and call k = 1
To the left
2/(1)^2 + 1/(1)^2 = 3/1 to the left
so we need 3 to the right
Qd/4^2 = 3
Qd = 16*3 = 48