Question

A small glass bead charged to 5.0 nCnC is in the plane that bisects a thin, uniformly charged, 10-cmcm-long glass rod and is 4.0 cmcm from the rod's center. The bead is repelled from the rod with a force of 840 μNμN.What is the total charge on the rod?

Answer 1

The total charge on the rod is 47.8 nC.

Step-by-step explanation:

Given that,

Charge = 5.0 nC

Length of glass rod= 10 cm

Force = 840 μN

Distance = 4.0 cm

The electric field intensity due to a uniformly charged rod of length L at a distance x on its perpendicular bisector

We need to calculate the electric field

Using formula of electric field intensity

`E=\frac{kQ}{x\sqrt{((L)/(2))^2+x^2}}`

Where, Q = charge on the rod

The force is on the charged bead of charge q placed in the electric field of field strength E

Using formula of force

`F=qE`

Put the value into the formula

`F=q*\frac{kQ}{x\sqrt{((L)/(2))^2+x^2}}`

We need to calculate the total charge on the rod

`Q=\frac{Fx\sqrt{((L)/(2))^2+x^2}}{kq}`

Put the value into the formula

`Q=\frac{840*10^(-6)*4.0*10^(-2)\sqrt{((10.0*10^(-2))/(2))^2+(4.0*10^(-2))^2}}{9*10^(9)*5.0*10^(-9)}`

`Q=47.8*10^(-9)\ C`

`Q=47.8\ nC`

Hence, The total charge on the rod is 47.8 nC.