A cylindrical cavity of diameter 'a' exists inside a cylinder of diameter '2a' as shown in the figure. Both the cylinder and the cavity are infinitely long. A uniform current density J flows along the length. If the magnitude of the magnetic field at the point P is given by , then the value of N is

Engineering

Physics

Magnetic Field

Question

A cylindrical cavity of diameter 'a' exists inside a cylinder of diameter '2a' as shown in the figure. Both the cylinder and the cavity are infinitely long. A uniform current density J flows along the length. If the magnitude of the magnetic field at the point P is given by $\frac{N}{12} μ_{0} aJ$ , then the value of N is

LiveFree JEE Main Previous Year Online Papers Live Free JEE Advance Previous Year Online Papers

College PredictorLive

Know your College Admission Chances Based on your Rank/Percentile, Category and Home State.

Get your JEE Main Personalised Report with Top Predicted Colleges in JoSA

$B_{P} = \frac{μ_{0} Ja}{2} - \frac{μ_{0} J π {(\frac{a}{2})}^{2}}{2 π \frac{3 a}{2}} = \frac{μ_{0} Ja}{2} [1 - \frac{1}{6}] = \frac{5 μ_{0} Ja}{12} ∴ N = 5$