If the current through a long solenoid is doubled while thecoil\'s length is als

Question

If the current through a long solenoid is doubled while thecoil's length is also doubled, keeping the total number of turnsconstant,the magnetic field at the point inside near the axisis a. four times larger   b. half the orginalsize c. unchanged     d. 1/4 thesize    If the current through a long solenoid is doubled while thecoil's length is also doubled, keeping the total number of turnsconstant,the magnetic field at the point inside near the axisis a. four times larger   b. half the orginalsize c. unchanged     d. 1/4 thesize   

Explanation / Answer

We know magnetic field B = Ni/ L

From this ( B ‘ / B ) = ( N ‘ / N ) ( I ‘ / I) ( L / L ‘ )

Given L ‘ = 2L

           N‘ = N

           I‘ = 2I

Plug the values we get B ‘ / B = 1* 2* ( 1/ 2)

                                               = 1

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