15 charges, each of value q are placed on X - axis at an equal distance 0.5R. The maximum electric flux associated with the spherical closed surface of radius 1.5R, in which one of the charges at the centre is .

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(1) (5q)/(ε₀). Given: 15 equal charges q in a row on the X-axis, adjacent ones 0.5R apart; a spherical surface of radius 1.5R centred on one of these charges. Idea: Gauss's law gives φ=(qᵢₙ)/(ε₀), where qᵢₙ is only the charge strictly inside the closed surface. Measured from whichever charge is at the centre, its neighbours lie at 0.5R, 1.0R, 1.5R, 2.0R, ... on each side. Strictly inside (<1.5R): the centre charge itself and those at ±0.5R and ±1.0R - that is 5 charges. The two at ±1.5R lie on the surface, not within it. The word maximum settles which charge to centre on: a charge near either end of the row has fewer than two neighbours on one side, so the count is largest for a charge well inside the row. φₘₐₓ=(5q)/(ε₀)

15 charges, each of value q are placed on X - axis at an equal distance 0.5R. The maximum electric flux associated with the spherical closed surface of radius 1.5R, in which one of the charges at the centre is ________.

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