Physics - Magnetism Question with Solution | TestHub

If we take a small strip of $dr$ at distancer from centre, then number of turns in this strip would be $$dN=\frac{N}{b-a}dr$$ Magnetic field due to this element at the centre of the coil will be $$\begin{array}{rl}& dB=\frac{{\mu }_0(dN)I}{2r}=\frac{{\mu }_{0}NI}{2(b-a)}\frac{dr}{r}\\ \therefore & B={\int }_{r=a}^{r=b}dB=\frac{{\mu }_{0}NI}{2(b-a)}\ln \frac{b}{a}\end{array}$$ $\therefore$ Correct answer is (a). Analysis of Question (i) If we see this problem independently, then I will rate this question moderately difficult. But the idea of this question is taken from question number $3.245$ of IE Irodov. (ii) Interestingly the same question was asked in IIT-JEE 2001 also.