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.

Question

A. -Q = -20 nC
B. -Q = -30 nC
C. -Q = +25 nC
D. -Q = -25 nC

Answer 1

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