Two coplanar concentric circular coils of radii r and text2 r , have the same number of turns n . The smaller coil carries a clockwise current i , while the larger coil carries an anticlockwise current text2 i . The magnetic field induction at the centre is

Question

Two coplanar concentric circular coils of radii r and text2 r , have the same number of turns n . The smaller coil carries a clockwise current i , while the larger coil carries an anticlockwise current text2 i . The magnetic field induction at the centre is (A) (3 μ 0 n i/4 r) (B) zero (C) (μ 0 n i/4 r) (D) (μ 0 n i/2 r)

Tardigrade Admin · Accepted Answer

B1=(μ0 n i/2 r), B2=(μ0 n(2 i)/2(2 r)) BR=B1-B2 B1=B2, both are in opposite direction

Q. Two coplanar concentric circular coils of radii $r$ and $2 r$ , have the same number of turns $n$ . The smaller coil carries a clockwise current $i$ , while the larger coil carries an anticlockwise current $2 i$ . The magnetic field induction at the centre is

$\frac{3 μ _{0} ni}{4 r}$

zero

$\frac{μ _{0} ni}{4 r}$

$\frac{μ _{0} ni}{2 r}$

$B_{1} = \frac{μ _{0} ni}{2 r}, B_{2} = \frac{μ _{0} n ( 2 i )}{2 ( 2 r )}$
$B_{R} = B_{1} - B_{2}$
$B_{1} = B_{2}$ , both are in opposite direction

Q. Two coplanar concentric circular coils of radii r and 2r , have the same number of turns n . The smaller coil carries a clockwise current i , while the larger coil carries an anticlockwise current 2i . The magnetic field induction at the centre is

4r3μ0​ni​

zero

4rμ0​ni​

2rμ0​ni​

B1​=2rμ0​ni​,B2​=2(2r)μ0​n(2i)​ BR​=B1​−B2​ B1​=B2​, both are in opposite direction

Q. Two coplanar concentric circular coils of radii $r$ and $2 r$ , have the same number of turns $n$ . The smaller coil carries a clockwise current $i$ , while the larger coil carries an anticlockwise current $2 i$ . The magnetic field induction at the centre is

$\frac{3 μ _{0} ni}{4 r}$

$\frac{μ _{0} ni}{4 r}$

$\frac{μ _{0} ni}{2 r}$

$B_{1} = \frac{μ _{0} ni}{2 r}, B_{2} = \frac{μ _{0} n ( 2 i )}{2 ( 2 r )}$
$B_{R} = B_{1} - B_{2}$
$B_{1} = B_{2}$ , both are in opposite direction