Q. A long solenoid has 200 turns/cm and carries a current $i.$ The magnetic field at its centre is $6.28 \times 10^{- 2}\ Wb/m^{2}.$ Another long solenoid has 100 turns/cm and it carries a current $i/3.$ The value of the magnetic field at its centre is
A) $1.05 \times 10^{- 2}\ {Wbm}^{- 2}$
B) $1.05 \times 10^{- 5}\ {Wbm}^{- 2}$
C) $1.05 \times 10^{- 3}\ {Wbm}^{- 2}$
D) $1.05 \times 10^{- 4}\ {Wbm}^{- 2}$
Explanation
(a) Magnetic field due to a long solenoid is given by
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ B = \mu_{0}ni$
From given data,
$6.28 \times 10^{- 2} = \mu_{0} \times 200 \times 10^{2} \times i$ …(i)
and $B = \mu_{0} \times 100 \times 10^{2} \times \left( \frac{i}{3} \right)$ …(ii)
Solving Eqs. (i) and (ii), we get
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ B = 1.05 \times 10^{- 2}\ Wb/m^{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.