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Naily
1 month ago
10

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?
Physics
1 answer:
Sav [3.1K]1 month ago
6 0

Answer:

The glass rod has a total charge of 47.8 nC.

Explanation:

Details provided:

Charge = 5.0 nC

Length of glass rod = 10 cm

Force = 840 μN

Distance = 4.0 cm

To evaluate the electric field intensity emitted by a uniformly charged rod of length L at a perpendicular distance from its midpoint

We will calculate the electric field

Using the formula for electric field intensity

E=\dfrac{kQ}{x\sqrt{(\dfrac{L}{2})^2+x^2}}

Where Q represents the charge on the rod

The force acting on the charged bead placed in the electric field of strength E

Using the force formula

F=qE

Insert the values into the formula

F=q\times\dfrac{kQ}{x\sqrt{(\dfrac{L}{2})^2+x^2}}

Now we calculate the total charge on the rod

Q=\dfrac{Fx\sqrt{(\dfrac{L}{2})^2+x^2}}{kq}

Substituting values into the equation

Q=\dfrac{840\times10^{-6}\times4.0\times10^{-2}\sqrt{(\dfrac{10.0\times10^{-2}}{2})^2+(4.0\times10^{-2})^2}}{9\times10^{9}\times5.0\times10^{-9}}

Q=47.8\times10^{-9}\ C

Q=47.8\ nC

Thus, the total charge on the rod is 47.8 nC.

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