Consider a long current carrying cylindrical conductor of radius R. Current density J inside the conductor is uniform over it’s cross-section. The magnitude of net contact force per unit length experienced by 14th of cylindrical conductor obtained by two mutually perpendicular planes containing the axis of cylinder intersecting each other is given by η(μ0J2R3). Find η.

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Consider a long current carrying cylindrical conductor of radius $R$ . Current density $J$ inside the conductor is uniform over it’s cross-section. The magnitude of net contact force per unit length experienced by $\frac{1}{4} th$ of cylindrical conductor obtained by two mutually perpendicular planes containing the axis of cylinder intersecting each other is given by $η (μ_{0} J^{2} R^{3}) .$ Find $η .$

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$F_{0} = \frac{μ_{0} J^{2} R^{3}}{6}, ∴ F_{n e t} = \sqrt{2} F_{0} .$

$η = \frac{\sqrt{2}}{6}$

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