Question

A long solenoid has $200$ turns per 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 per cm and it carries a current $i/3$ . The value of the magnetic field at its centre is

• A. $1.05\times 10^{-2}Wb/m^2$
• B. $1.05\times 10^{-5}Wb/m^2$
• C. $1.05\times 10^{-3}Wb/m^2$
• D. $1.05\times 10^{-4}Wb/m^2$

Answer 1

Answer: (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 $B={\mu }_0\times 100\times 10^2\times (i/3)$ ...(ii)
Solving Eqs. (i) and (ii), we get
$B\approx 1.05\times 10^{-2}Wb/m^2$