Question

Which of the following graphs correctly represent the variation of magnetic field $\left(B\right)$ inside a finite length solenoid with respect to distance $x$ from its center. The current in solenoid having $n$ turns per unit length is $i$.

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

The magnetic filed at a point inside the finite length solenoid is given by,

$B=\frac{{\mu }_{0}ni}{2}[\cos {\theta }_1-\cos {\theta }_2]$

For a point at the center of solenoid

${\theta }_1=0^{\circ }\text{and}{\theta }_2={180}^{\circ }$

$B=\frac{{\mu }_{0}ni}{2}[\cos 0^{\circ }-\cos {180}^{\circ }]=\frac{{\mu }_{0}ni}{2}[1-(-1\left)\right]$

$\therefore B={\mu }_{0}ni$

Thus, the magnetic field is maximum at center, and it will decrease symmetrically on both side of center.

The value of magnetic field drops significantly as the point moves further apart the half-length distance.

Hence, option $\left(d\right)$ gives correct representation.