If in a circular coil A of radius R, current i is flowing and in another coil B of radius 2R , a current 2i is flowing, then the ratio of the magnetic fields, BA and BB produced by them at their centres will be:

Question

If in a circular coil A of radius R, current i is flowing and in another coil B of radius 2R , a current 2i is flowing, then the ratio of the magnetic fields, BA and BB produced by them at their centres will be: (A) 1 (B) 2 (C) (1/2) (D) 4

Tardigrade Admin · Accepted Answer

Magnetic field in circular coil A is Similarly, BA=(μ 0 N i/2 R) R is radius and i is current flowing in coil. BB=((μ )0 N (. 2 i .)/2 . (. 2 R .)) =(μ 0 N i/2 R) (BA/BB)=(1/1)=1

Q. If in a circular coil $A$ of radius $R,$ current $i$ is flowing and in another coil $B$ of radius $2 R$ , a current $2 i$ is flowing, then the ratio of the magnetic fields, $B_{A}$ and $B_{B}$ produced by them at their centres will be:

$1$

$2$

$\frac{1}{2}$

$4$

Magnetic field in circular coil $A$ is
Similarly, $B_{A} = \frac{μ _{0} N i}{2 R}$
$R$ is radius and $i$ is current flowing in coil.
$B_{B} = \frac{( μ ) _{0} N ( 2 i )}{2 . ( 2 R )}$
$= \frac{μ _{0} N i}{2 R}$
$\frac{B _{A}}{B _{B}} = \frac{1}{1} = 1$

Q. If in a circular coil A of radius R, current i is flowing and in another coil B of radius 2R , a current 2i is flowing, then the ratio of the magnetic fields, BA​ and BB​ produced by them at their centres will be:

1

2

21​

4

Magnetic field in circular coil A is Similarly, BA​=2Rμ0​Ni​ R is radius and i is current flowing in coil. BB​=2.(2R)(μ)0​N(2i)​ =2Rμ0​Ni​ BB​BA​​=11​=1

Q. If in a circular coil $A$ of radius $R,$ current $i$ is flowing and in another coil $B$ of radius $2 R$ , a current $2 i$ is flowing, then the ratio of the magnetic fields, $B_{A}$ and $B_{B}$ produced by them at their centres will be:

$1$

$2$

$\frac{1}{2}$

$4$

Magnetic field in circular coil $A$ is
Similarly, $B_{A} = \frac{μ _{0} N i}{2 R}$
$R$ is radius and $i$ is current flowing in coil.
$B_{B} = \frac{( μ ) _{0} N ( 2 i )}{2 . ( 2 R )}$
$= \frac{μ _{0} N i}{2 R}$
$\frac{B _{A}}{B _{B}} = \frac{1}{1} = 1$