KVPY 2020-21 SB SX Exam Previous Papers

Question : 97 of 120

Marks: +1, -0

A beam of neutrons performs circular motion of radius,

{r}=1 {m}

, under the influence of an inhomogeneous magnetic field with inhomogeneity extending over

\Δ{r}=0.01 {m}

. The speed of the neutrons is

54 {m} \/ {s}

. The mass and magnetic moment of the neutrons respectively are

1.67 \×10^{-27} {kg}

and

9.67 \×10^{-27} {J} \/ {T}

. The average variation of the magnetic field over

\Δ{r}

is approximately.

Solution:

{F}={M} {𝜕{B}}/{𝜕{r}}={{mv}^{2}}/{{r}}

\Δ {B}={{mv}^{2}}/{{Mr}} \Δ{r}

={1.67 \×10^{-27} \×54^{2} \×0.01}/{9.67 \×10^{-27} \×1}

=5.03 {T}

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