Solveeit Logo
Login

Question

Question: The magnetic induction at a point 1 ![](https://cdn.pureessence.tech/canvas_33.png?top_left_x=1500&t...

The magnetic induction at a point 1 away from a proton measured along its axis of spin is

(magnetic moment of the proton is 1.4 x l0-26 A m2)

A

0.28 mT

B

28 mT

C

0.028 mT

D

2.8 mT

Answer

2.8 mT

Explanation

Solution

: On the axis of a magnetic dipoles, magnetic induction is,

B=μ04π×2 mr3\mathrm { B } = \frac { \mu _ { 0 } } { 4 \pi } \times \frac { 2 \mathrm {~m} } { \mathrm { r } ^ { 3 } }

Here, r=1A˚=10−10 m, m=1.4×10−26Am2\mathrm { r } = 1 \AA = 10 ^ { - 10 } \mathrm {~m} , \mathrm {~m} = 1.4 \times 10 ^ { - 26 } \mathrm { Am } ^ { 2 } and

∴B=10−7×2×1.4×10−26(10−10)3\therefore \mathrm { B } = \frac { 10 ^ { - 7 } \times 2 \times 1.4 \times 10 ^ { - 26 } } { \left( 10 ^ { - 10 } \right) ^ { 3 } }

=10−7×2.8×10−2610−30=2.8×10−3 T=2.8mT= \frac { 10 ^ { - 7 } \times 2.8 \times 10 ^ { - 26 } } { 10 ^ { - 30 } } = 2.8 \times 10 ^ { - 3 } \mathrm {~T} = 2.8 \mathrm { mT }