A long cylindrical conductor of radius R has two cylindrical cavities of diameter R as shown and carries uniform current density J. At Q (x=2R), B=(α/68)μ₀JR. Find α.

Question

G1 Physics · Accepted Answer

Use superposition: field of the full current-filled cylinder plus two negative-current cylinders representing the cavities. Evaluate each contribution at Q using the inside/outside cylinder formulas and vector addition. The resultant is B=(9/68)μ₀JR, so α=9.