The magnetic induction at a point P which is at the . . .

Question : The magnetic induction at a point P which is at the distance of 4 cm from a long current carrying wire is 10^-3T. The field of induction at a distance 12 cm from the current will be 

a) 3.33×10^-4 T

b) 1.11×10^-4 T

c) 33×10^-3 T

d) 9×10^-3 T

Doubt by Trishna

Solution : 

Note : Here the meaning of "field of induction" is same as "magnetic field".

We know, magnetic field due a current carrying conductor at a point is given by 

B=µ₀I/2πr

Here

r₁=4cm

r₂=12 cm

B₁=10-3T

B₂=?

B₁=µ₀I/2πr₁ — (1)

B₂=µ₀I/2πr₂ — (2)

Dividing equation (2) by (1)

B₂/B₁=r₁/r₂

B₂/B₁=4/12

B₂/B₁=1/3

B₂=B₁/3

B₂=(10^-3)/3

B₂=0.333×10^-3

B₂=3.33×10^-4 T

Hence, a) 3.33×10^-4 T would be the correct option.