Electric charge is uniformly distributed along a long straight wire of radius 1m

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Electric charge is uniformly distributed along a long straight wire of radius 1mm. The charge per cm length of the wire is Q coulomb. Another cylindrical surface of radius 50 cm and length 1m symmetrically encloses the wire as shown in the figure. The total electric flux passing through the cylindrical surface is

Electric Charge Is Uniformly Distributed Along A Long Straig...

Options:

A . Qϵ0

B . 100Qϵ0

C . 10Q(πϵ0)

D . 100Q(πϵ0)

Answer: Option B
:
B
Charge enclosed by cylindrical surface (length 100 cm) is

Q_{e x c} = 100 Q .

By applying Gauss's law

ϕ = \frac{1}{ϵ_{0}} (Q_{e γ α}) = \frac{1}{ϵ_{0}} (100 Q)

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