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A hollow cylinder has a charge q coulomb within it. If Φ is the electric flux in units of voltmeter associated with the curved surface B, the flux linked with the plane surface in units of voltmeter will be.


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Solution

Step 1. Given data

The charge of the hollow cylinder is q

Flux=Φ

Step 2. Formula used

According to Gaussian Law, we know that the total electric flux out in a closed surface is equal to the charge enclosed divided by the permeability

Φ=qε0

Where Φ is the electric flux, q is the charge enclosed and ε0 is the permittivity of free space,

Step 3. Net flux through the surface

Let the flux of the surface A,B and C is ΦA,ΦB and ΦC

Given that the electric flux in the hollow cylinder is =Φ

All the three points are in same hollow cylinder, so the net flux is equal to the sum of the individual flux

Φ=ΦNet=ΦA+ΦB+ΦC

Step 4. Flux through surface A ,Band C

The ends of the hollow cylinder are A and C so the flux in these two point are same.

ΦA=ΦC

The net flux is equal to the flux of B then

Also Φ=ΦB

Step 5. Find the flux linked with the plane surface A

ΦA+ΦB+ΦC=qε02ΦA+Φ=qε0ΦC=ΦAandΦB=ΦΦA=12qε0-Φ

Hence the flux through the surface A is 12qε0-Φ


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