A long straight wire of radius a carries a steady current I. The current uniformly distributed over its cross-section. The ratio of the magnetic fields B and B', at radial distance (a/2) and 2a respectively, from the axis of the wire is :

Question

A long straight wire of radius a carries a steady current I. The current uniformly distributed over its cross-section. The ratio of the magnetic fields B and B', at radial distance (a/2) and 2a respectively, from the axis of the wire is : (A) (1/2)  (B) 1 (C) 4 (D) (1/4)

Tardigrade Admin · Accepted Answer

For points inside the wire B = (μ0 I r/2 π R2) (r le R) For points outside the wire B = (μ0 I/2 π r) (r ge R) according to the question (B/B') = ((μ0 I (a /2)/2 π a2)/(μ0 I )2 π(2a)) = 1: 1

Q. A long straight wire of radius a carries a steady current I. The current uniformly distributed over its cross-section. The ratio of the magnetic fields B and B', at radial distance $\frac{a}{2}$ and 2a respectively, from the axis of the wire is :

$\frac{1}{2}$

1

4

$\frac{1}{4}$

For points inside the wire
$B = \frac{μ _{0} I r}{2 π R ^{2}} (r \leq R)$
For points outside the wire
$B = \frac{μ _{0} I}{2 π r} (r \geq R)$
according to the question
$\frac{B}{B ^{'}} = \frac{\frac{μ _{0} I ( a /2 )}{2 π a ^{2}}}{\frac{μ _{0} I}{2 π ( 2 a )}} = 1 : 1$

Q. A long straight wire of radius a carries a steady current I. The current uniformly distributed over its cross-section. The ratio of the magnetic fields B and B', at radial distance 2a​ and 2a respectively, from the axis of the wire is :

21​

1

4

41​

For points inside the wire B=2πR2μ0​Ir​(r≤R) For points outside the wire B=2πrμ0​I​(r≥R) according to the question B′B​=2π(2a)μ0​I​2πa2μ0​I(a/2)​​=1:1

Q. A long straight wire of radius a carries a steady current I. The current uniformly distributed over its cross-section. The ratio of the magnetic fields B and B', at radial distance $\frac{a}{2}$ and 2a respectively, from the axis of the wire is :

$\frac{1}{2}$

$\frac{1}{4}$

For points inside the wire
$B = \frac{μ _{0} I r}{2 π R ^{2}} (r \leq R)$
For points outside the wire
$B = \frac{μ _{0} I}{2 π r} (r \geq R)$
according to the question
$\frac{B}{B ^{'}} = \frac{\frac{μ _{0} I ( a /2 )}{2 π a ^{2}}}{\frac{μ _{0} I}{2 π ( 2 a )}} = 1 : 1$