A copper wire having resistance 0.01 ohm  in each metre is used to wind a 400 –turn solenoid of radius  1.0cm and length 20 cm. Find the emf of a battery (in volt) which when connected across the solenoid will cause a magnetic field of 1.0×10−2 T near the centre of the solenoid.

A copper wire having resistance 0.01ohm  in each metre is used to wind a 400 –turn solenoid of radius  1.0cm and length 20 cm. Find the emf of a battery (in volt) which when connected across the solenoid will cause a magnetic field of 1.0×102 T near the centre of the solenoid.

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    Solution:

    Resistance per unit length = Rl=0.01Ω m-1,r=1.0cm Total turns =400,=20cm,B=1×102T,n=40020×102 turns /mi=ER0=ERl×(2πr×400)=E0.01×2×π×0.01×400B=μ0ni10-2=4π×107×40020×102×E400×2π×0.01×102
    E=102×20×102×400×2π×102×0.014π×107×400=1V

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