Answer:
The total charge on the rod is 41.18 nC
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;
[tex]F = \frac{K[q_1][q_2]}{R^2}[/tex]
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; [tex]R^2= r(\sqrt{r^2 +(\frac{L}{2})^2}[/tex]
K is coulomb's constant = 8.99 x 10⁹ Nm²/C²
[tex]F = \frac{K(q)Q}{r\sqrt{r^2 +(\frac{L}{2})^2} } \\\\940 X 10^{-6}= \frac{8.99 X10^ 9(6.5X10^{-9})Q}{0.04\sqrt{(0.04)^2 +(\frac{0.1}{2})^2}} \\\\940 X 10^{-6} =\frac{(58.435)Q}{0.00256} \\\\(58.435)Q = 940 X 10^{-6} *0.00256\\\\(58.435)Q = 2.406X10^{-6}\\\\Q =\frac{2.406X10^{-6}}{58.435}\\\\ Q = 4.118 X10^{-8} C= 41.18 nC[/tex]
Therefore, the total charge on the rod is 41.18 nC
