Question

A small glass bead charged to 6.5 nC is in the plane that bisects a thin, uniformly charged, 10-cm-long glass rod and is 4.0 cm from the rod's center. The bead is repelled from the rod with a force of 940 μN.

Part A

What is the total charge on the rod?

Express your answer with the appropriate units.

Answer 1

The total charge on the rod is 41.18 nC

Step-by-step explanation:

Given;

length of glass rod, L = 10 cm = 0.1 m

radius of the rod, r = 4 cm = 0.04 m

Force of repulsion = 940 μN = 940 × 10⁻⁶ N

Charge on the bead = 6.5 nC = 6.5 × 10⁻⁹ C

Charge on the rod, Q = ?

From coulomb's law;

`F = (K[q_1][q_2])/(R^2)`

Where;

F is the force of repulsion in N

q₁ and q₂ are the charges on the bead and rod

R is the resultant distance between the two charges;
`R^2= r(\sqrt{r^2 +((L)/(2))^2}`

K is coulomb's constant = 8.99 x 10⁹ Nm²/C²

`F = \frac{K(q)Q}{r\sqrt{r^2 +((L)/(2))^2} } \\\\940 X 10^(-6)= \frac{8.99 X10^ 9(6.5X10^(-9))Q}{0.04\sqrt{(0.04)^2 +((0.1)/(2))^2}} \\\\940 X 10^(-6) =((58.435)Q)/(0.00256) \\\\(58.435)Q = 940 X 10^(-6) *0.00256\\\\(58.435)Q = 2.406X10^(-6)\\\\Q =(2.406X10^(-6))/(58.435)\\\\ Q = 4.118 X10^(-8) C= 41.18 nC`

Therefore, the total charge on the rod is 41.18 nC