In the figure,all the charges are point charges and the charge in the middle is Q = -3.1 nC.For what charge q₁ will charge q₂ be in static equilibrium? A) 12 nC B) 6.2 nC C) 3.1 nC D) 25 nC

Question

Quizplus · Accepted Answer

To find the charge qS1U1B11S1U1B0 that will balance the -3.1 nC charge at the center, we need to consider the forces acting on qS1U1B12S1U1B0 charge. There will be repulsive forces from the other two positive charges, qS1U1B11S1U1B0 and qS1U1B12S1U1B0, and an attractive force from the negative charge Q at the center.

For the system to be in equilibrium, the net force acting on the charge qS1U1B12S1U1B0 must be zero. This means that the repulsive forces from qS1U1B11S1U1B0 and qS1U1B12S1U1B0 must be equal and opposite to the attractive force from Q at the center.

Let's first consider just the horizontal forces. Since qS1U1B11S1U1B0 and qS1U1B12S1U1B0 have the same charge, the repulsive forces will have the same magnitude. From symmetry, we can see that these two forces will cancel each other out horizontally. Therefore, there will only be a net force in the vertical direction.

The vertical component of the repulsive force will be F = k*q1*q2/r^2, where k is Coulomb's constant, q1 and q2 are the charges on the two objects, and r is the distance between them. Since qS1U1B11S1U1B0 and qS1U1B12S1U1B0 are equally distant from qS1U1B22S1U1B0, we can write:

F_repulsive = k*qS1U1B12S1U1B0*qS1U1B11S1U1B0/r^2

The attractive force from the negative charge Q at the center is:

F_attractive = k*Q*qS1U1B12S1U1B0/r^2

For equilibrium, these two forces must be equal in magnitude:

k*qS1U1B12S1U1B0*qS1U1B11S1U1B0/r^2 = k*Q*qS1U1B12S1U1B0/r^2

qS1U1B11S1U1B0 = Q = -3.1 nC

Substituting this value, we get:

qS1U1B12S1U1B0 = -qS1U1B11S1U1B0/qS1U1B11S1U1B0

qS1U1B12S1U1B0 = -(-3.1 nC) = 3.1 nC

However, this is only the magnitude of the charge qS1U1B12S1U1B0. The question asks for the actual charge, which could be positive or negative. Since qS1U1B11S1U1B0 is negative, the charge qS1U1B12S1U1B0 must be positive to balance it. Therefore, the answer is:

Answer: A) 12 nC

In the Figure,all the Charges Are Point Charges and the Charge