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Q.

The volume charge density as a function of distance ‘x’ from one face inside a cube of side length ‘a’ varies as shown in the figure. Then the total flux in SI units through the cube is na2ρo4εo. Find n.

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answer is 3.

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Detailed Solution

From Gauss law, Electric flux=Charge enclosedε0

φ=∫ρa2dxε0=a2∫ρdxε0=a2(area  under   ρ−x graph)ε0=3a2ρ04ε0.

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