Question

There are $50$ turns of a wire in every cm length of a long solenoid.If $4A$ currents is following in the solenoid,the approximate value of magnetic field along its axis at an internal point and at one end will be respectively.

• A. $12.6\times {10}^{-3}Wb/m^2,6.3\times {10}^{-3}Wb/m^2$
• B. $12.6\times {10}^{-3}Wb/m^2,25.1\times {10}^{-3}Wb/m^2$
• C. $25.1\times {10}^{-3}Wb/m^2,12.6\times {10}^{-3}Wb/m^2$
• D. $25.1\times {10}^{-5}Wb/m^2,12.6\times {10}^{-5}Wb/m^2$

Answer 1

Answer: (C)

$25.1\times {10}^{-3}Wb/m^2,12.6\times {10}^{-3}Wb/m^2$

The magnetic field in the solenoid along its axis (i) At an internal point $={\mu }_{0}ni$

$=4\pi \times {10}^{-7}\times 5000\times 4=25.1\times {10}^{-3}Wb/m^2$

( Here $n=50turns/cm=5000turns/m$)

(ii) At one end

$B_{end}=\frac{1}{2}{B}_{in}=\frac{{\mu }_{0}ni}{2}$

$=\frac{25.1\times {10}^{-3}}{2}=12.6\times {10}^{-3}Wb/m^2$