Two small beads having positive charges q1 = 34.0 nC and q2 = 55.0 nC are fixed so that the centers of the two beads are separated by a distance d = 0.450 m as shown in the figure. At what position x relative to q1 could you place a third small bead of unknown charge q in order for it to be in equilibrium? Answer in units of meters.

Question

Two small beads having positive charges q1 = 34.0 nC and q2 = 55.0 nC are fixed so that the centers of the two beads are separated by a distance d = 0.450 m as shown in the figure. At what position x relative to q1 could you place a third small bead of unknown charge q in order for it to be in equilibrium? Answer in units of meters.

Answer 1

if they are in a straight line, then the forces on q3 are balanced, that is possible to do this by placing a positive (or negative) charge q3 in between so the forces are balanced both ways.

ForceLeft=ForceRight
kq1q3/x^2=kq2q3/(.45-x)^2

(.45-x)^2= q2/q1 ( x^2)

expand all that to a quadratic, and solve for x.

Answer 2

To determine the position x relative to q1 where the third bead should be placed for equilibrium, we need to consider the electrical forces acting on it.

Let's start by calculating the electric force between q1 and q3. The equation for the electric force between two point charges is given by Coulomb's Law:

F1-3 = k * |q1| * |q3| / r1-3^2

where F1-3 is the force between q1 and q3, k is the electrostatic constant (k = 9.0 x 10^9 Nm^2/C^2), |q1| and |q3| are the magnitudes of the charges, and r1-3 is the distance between them.

Since we want the third bead to be in equilibrium, the forces acting on it should balance out. This means that the electric force between q2 and q3 should be equal in magnitude but opposite in direction to the electric force between q1 and q3.

Now, let's calculate the electric force between q2 and q3. Using Coulomb's Law again:

F2-3 = k * |q2| * |q3| / r2-3^2

where F2-3 is the force between q2 and q3, |q2| is the magnitude of the charge on q2, and r2-3 is the distance between them.

For equilibrium, F1-3 and F2-3 should be equal in magnitude:

F1-3 = F2-3

By substituting the expressions for the forces, we get:

k * |q1| * |q3| / r1-3^2 = k * |q2| * |q3| / r2-3^2

Now, we can simplify further:

|q1| / r1-3^2 = |q2| / r2-3^2

Since the distances, r1-3 and r2-3, are given as d and x, respectively, we can rewrite the equation as:

|q1| / d^2 = |q2| / x^2

Now, we can rearrange the equation to solve for x:

x^2 = (|q2| * d^2) / |q1|

Finally, taking the square root of both sides gives us the position x relative to q1:

x = sqrt((|q2| * d^2) / |q1|)

Plugging in the given values: q1 = 34.0 nC, q2 = 55.0 nC, and d = 0.450 m, we can calculate the value of x.

if they are in a straight line, then the forces on q3 are balanced, that is possible to do this by placing a positive (or negative) charge q3 in between so the forces are balanced both ways.

Vabndg

To determine the position x relative to q1 where the third bead should be placed for equilibrium, we need to consider the electrical forces acting on it.