A long solenoid is wound in two separate sections placed end-to-end along the same axis

PHYSICS · Multi-part · CBSE · Physics · Moving Charges and Magnetism · Moving Charges and Magnetism

Problem

A 0.60 m0.60\,\text{m} long solenoid is wound in two separate sections placed end-to-end along the same axis. In the first 0.20 m0.20\,\text{m} length the winding density is n1=1.0×103  turns m−1n_1=1.0\times10^{3}\;\text{turns m}^{-1}, while in the remaining 0.40 m0.40\,\text{m} length it is n2=2.0×103  turns m−1n_2=2.0\times10^{3}\;\text{turns m}^{-1}. The same steady current I=2.0 AI=2.0\,\text{A} flows through all turns. (i) Obtain expressions for the magnitude of the magnetic field in each of the two sections of the solenoid, treating each section as long compared to its radius. (ii) Calculate the numerical values of the fields in the two sections for air core (μr=1)(\mu_r=1). State their units. (iii) Sketch qualitatively the variation of the field magnitude BB with distance measured along the axis from the start of the first section to the end of the second section. Mark all significant values on your sketch.

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