JEE Main 2022 · 30 Jun · Shift 1 · Physics Q39

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PhysicsSingle correct+4 / -1Question 39 of 90

A coil of n number of turns wound tightly in the form of a spiral with inner and outer radii $r_1$ and $r_2$ respectively. When a current of strength I is passed through the coil, the magnetic field at its centre will be :

\dfrac{\mu_0nI}{2(r_2-r_1)}

\dfrac{\mu_0nI}{r_2}

\dfrac{\mu_0nI}{r_2-r_1}\log_e\dfrac{r_1}{r_2}

\dfrac{\mu_0nI}{2(r_2-r_1)}\log_e\dfrac{r_2}{r_1}

Answer and worked solution

Official answer: D

Rings between $r$ and $r+dr$ carry $\frac{nI\,dr}{r_2-r_1}$ turns' current: $B=\displaystyle\int_{r_1}^{r_2}\frac{\mu_0nI\,dr}{2(r_2-r_1)r}=\frac{\mu_0nI}{2(r_2-r_1)}\ln\frac{r_2}{r_1}$ .

(D)

Topics:Biot-Savart law

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JEE Main 2022 · 30 Jun · Shift 1, Physics question 39