Question

What is the maximum possible value of a magnetic field at a point inside a solenoid?

• A. ${\mu }_{0}ni/2$
• B. $2{\mu }_{0}ni$
• C. $0$
• D. ${\mu }_{0}ni$

Answer 1

The correct option is D ${\mu }_{0}ni$

We know that a magnetic field at a point inside a solenoid is given by,

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

To have maximum value of $B$,

$(\cos {\theta }_1-\cos {\theta }_2{)}_{max}=2$

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

$\therefore B_{max}=\frac{{\mu }_{0}ni}{2}\times 2={\mu }_{0}ni$

Therefore, option $\left(d\right)$ is correct.