A small glass bead has been charged to+ 25 nC . a tiny ball bearing 3.0 cmcm above the bead feels a 1.4*10^2 nn downward electric force.
A. -Q = -20 nC
B. -Q = -30 nC
C. -Q = +25 nC
D. -Q = -25 nC
Given that the tiny ball bearing feels a downward electric force, we can determine the sign and magnitude of the charge on the bead.
The electric force between two charged objects can be calculated using Coulomb's law:
Electric force = (k * |Q1 * Q2|) / r^2
Where:
- k is the electrostatic constant (8.99 x 10^9 Nm^2/C^2)
- |Q1| and |Q2| are the magnitudes of the charges on the objects
- r is the distance between the charges
In this case, the electric force is given as -1.4 x 10^2 N and the distance is 3.0 cm (0.03 m).
Plugging in the values into Coulomb's law equation, we get:
-1.4 x 10^2 N = (8.99 x 10^9 Nm^2/C^2) * (|Qbead| * |Qball bearing|) / (0.03 m)^2
Simplifying this equation, we can solve for |Qbead|:
|Qbead| * |Qball bearing| = -1.4 x 10^2 N * (0.03 m)^2 / (8.99 x 10^9 Nm^2/C^2)
|Qbead| * |Qball bearing| = -1.4 x 10^2 N * 9 x 10^-4 m^2 / 8.99 x 10^9 Nm^2/C^2
|Qbead| * |Qball bearing| = -1.4 x 9 x 10^-2 N * m^2 / 8.99 x 10^9 C^2
|Qbead| * |Qball bearing| = -11.88 x 10^-10 C^2 / 8.99 x 10^9 C^2
|Qbead| * |Qball bearing| = -1.32 x 10^-19 C^2
Since |Qball bearing| is not given, we cannot determine the exact value of |Qbead|. However, we can determine its sign based on the fact that the electric force is attractive (negative).
Therefore, the correct answer is:
D. -Q = -25 nC
To solve this problem, we can use the principle of electric force between two charged objects.
The formula for the electric force between two charged objects is given by:
F = (k * |Q1 * Q2|) / r^2,
where F is the electric force, k is the electrostatic constant (9 * 10^9 Nm^2/C^2), Q1 and Q2 are the charges on the two objects, and r is the distance between the two objects.
From the given information, Q1 = +25 nC (positive charge on the glass bead), F = 1.4 * 10^2 nN (downward electric force), and r = 3.0 cm = 3.0 * 10^-2 m.
Plugging these values into the formula, we can solve for Q2 (the charge on the tiny ball bearing):
1.4 * 10^2 nN = (9 * 10^9 Nm^2/C^2) * |(+25 nC) * Q2| / (3.0 * 10^-2 m)^2.
Simplifying the equation:
1.4 * 10^2 nN = (9 * 10^9 Nm^2/C^2) * 25 nC * |Q2| / (3.0 * 10^-2 m)^2.
Rearranging the equation:
|Q2| = (1.4 * 10^2 nN * (3.0 * 10^-2 m)^2) / ((9 * 10^9 Nm^2/C^2) * 25 nC).
Solving for |Q2|:
|Q2| ≈ 3.78 * 10^-11 C.
Since the force is downward, Q2 must be negative. Therefore, the correct answer is:
D. -Q = -25 nC.