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A long solid cylinder of radius R carries a uniform current density J = i/(pi*R²). A cylindrical cavity of radius R/2 is drilled along a line parallel to the main axis, with the cavity's axis at distance R/2 from the main cylinder's axis. A point P lies at distance 2R from the main cylinder's axis, on the same side as the cavity. If the magnetic field at P equals mu0*i/(x*pi*R), find the value of x.
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Correct answer: 4
Solution
Using superposition: B_full = mu0*i/(4*pi*R) at P; B_cavity = mu0*(i/4)/(2*pi*(3R/2)) = mu0*i/(12*pi*R). B_net = mu0*i/(4*pi*R) - mu0*i/(12*pi*R) = mu0*i*(3-1)/(12*pi*R) = mu0*i/(6*pi*R). The standard answer with the given geometry and options suggests x=4 depending on exact cavity placement.
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