Question

The relative permeability of the material of the core of a solenoid is \(400\) and the number of turns per metre of the solenoid is \(900\). If the windings of the solenoid are insulated from the core and a current of \(1.5\,\mathrm{A}\) is passed through the solenoid, then its magnetic intensity is

• A. \(1350\,\mathrm{A\,m^{-1}}\)
• B. \(600\,\mathrm{A\,m^{-1}}\)
• C. \(1.66\times10^{-3}\,\mathrm{A\,m^{-1}}\)
• D. \(0.678\,\mathrm{A\,m^{-1}}\)

Hint:

Inside a long solenoid, \[ \boxed{ H=nI } \] and the magnetic flux density is \[ \boxed{ B=\mu_0\mu_rH. } \] The value of \(H\) does not depend on the core material.

Answer 1

The Correct Option is A

Step 1: Use the expression for magnetic field intensity. The magnetic intensity inside a solenoid is \[ H=nI, \] where \[ n=900\,\mathrm{m^{-1}}, \qquad I=1.5\,\mathrm{A}. \] Note that \(H\) is independent of the relative permeability of the core.

Step 2: Calculate \(H\). \[ H = 900\times1.5 = 1350\,\mathrm{A\,m^{-1}}. \] Hence, \[ \boxed{1350\,\mathrm{A\,m^{-1}}} \] Therefore, \[ \boxed{(A)} \] is the correct answer.