Question 185: Magnetism and Matter

Question

A long, straight wire of radius a carries a current
distributed uniformly over its cross-section. The
ratio of the magnetic fields due to the wire at
distance
$${a \over 3}$$
and 2$$a$$, respectively from the axis
of the wire is :

Accepted Answer

Let current density be J.
$$ 	herefore $$ Applying Ampere's law. For point P
$$\oint {\overrightarrow {B.} d\overrightarrow l }  = {\mu _0}i$$
$$ \Rightarrow $$ B
P
2$$\pi $$$${a \over 3}$$ = $${\mu _0}J\pi {{{a^2}} \over 9}$$ ...(1)
$$ 	herefore $$ Applying Ampere's law. For point Q
B
Q
2$$\pi $$$${(2a)}$$ = $${\mu _0}J\pi {a^2}$$ ...(2)
Dividing (1) by (2) we get
$${{{B_P}2\pi {a \over 3}} \over {{B_Q}4\pi a}} = {{{\mu _0}J\pi {{{a^2}} \over 9}} \over {{\mu _0}J\pi {a^2}}}$$
$$ \Rightarrow $$ $${{{B_P}} \over {{B_Q}}} = {2 \over 3}$$

Answer

2

Answer

$${1 \over 2}$$

Answer

$${3 \over 2}$$

Answer

$${2 \over 3}$$

Magnetism and Matter

A long, straight wire of radius a carries a current distributed uniformly over its cross-section. The ratio of the magnetic fields due to the wire at distance ${a \over 3} and 2a$, respectively from the axis of the wire is :

Choose the correct answer: