Explanation:
It is given that, a long, straight wire is surrounded by a hollow metal cylinder whose axis coincides with that of the wire.
The charge per unit length of the wire is
and the net charge per unit length is
.
We know that there exist zero electric field inside the metal cylinder.
(a) Using Gauss's law to find the charge per unit length on the inner and outer surfaces of the cylinder. Let
are the charge per unit length on the inner and outer surfaces of the cylinder.
For inner surface,



For outer surface,



(b) Let E is the electric field outside the cylinder, a distance r from the axis. It is given by :


Hence, this is the required solution.
Answer:
The value of third charge is 0.8μC.
Explanation:
Given that.
Magnitude of net force=4.444 N
According to figure,
Suppose, First charge = 2.4 μC
Second charge = 6.2 μC
Distance r₁ = 9.8 cm
Distance r₂ = 2.1 cm
We need to calculate the value of r
Using Pythagorean theorem

Put the value into the formula


We need to calculate the force
Using formula of force

Force F₁₂,



Force F₂₃,

We need to calculate the value of third charge





Hence, The value of third charge is 0.8μC.
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