bead with a mass of 0.090g and a charge of 10nC is free to slide on a vertical rod. at the base of the rod is a fixed 10nC charge. in equilibrium, at what height above the fixed charge does the bead rest
Search instead for a bead with a mass of 0.090g and a charge of 10nC is free to slide on a vertical rod. at the base of the rod is a fixed 10nC charge. in equiliburim, at what height above the fixed charge does the bead rest
To find the height above the fixed charge where the bead rests in equilibrium, we need to consider the electrostatic force and the gravitational force acting on the bead.
1. Gravitational force:
The gravitational force acting on the bead is given by the equation:
F_grav = m * g
Where m is the mass of the bead and g is the acceleration due to gravity. In this case, the mass of the bead is 0.090g and the acceleration due to gravity is approximately 9.8 m/s^2.
2. Electrostatic force:
The electrostatic force between two charges is given by Coulomb's law:
F_elec = k * (|q1| * |q2|) / r^2
Where k is the electrostatic constant (approximately 9 x 10^9 Nm^2/C^2), q1 and q2 are the magnitudes of the charges, and r is the distance between the charges.
In this case, the magnitude of both charges is 10nC (nanoCoulombs) each, and the distance between them is the height above the fixed charge where the bead rests (h).
3. Equilibrium condition:
In equilibrium, the gravitational force and the electrostatic force are equal:
F_grav = F_elec
Now, to find the height above the fixed charge where the bead rests, we can set up the equation and solve for h:
m * g = k * (|q1| * |q2|) / r^2
Plugging in the known values:
0.090g * 9.8m/s^2 = (9 x 10^9 Nm^2/C^2) * (10nC * 10nC) / (h^2)
Simplifying the equation, we get:
0.882 * 10^(-3) kg*m^2/s^2 = (9 x 10^9) * (10^(-8)) C^2 / (h^2)
Solving for h^2:
h^2 = (9 x 10^9) * (10^(-8)) C^2 /(0.882 * 10^(-3)) kg*m^2/s^2
Finally, calculating the square root of both sides to find h:
h = sqrt[(9 x 10^9) * (10^(-8)) C^2 / (0.882 * 10^(-3)) kg*m^2/s^2]
Evaluating this expression gives the height above the fixed charge where the bead rests in equilibrium.