In the diagram I1,I2 are the strength of the currents in the loop and straight conductors respectively OA = AB = R. The net magnetic field at the centre O is zero. Then the ratio of the currents in the loop and the straight conductors is

Question

In the diagram I1,I2 are the strength of the currents in the loop and straight conductors respectively OA = AB = R. The net magnetic field at the centre O is zero. Then the ratio of the currents in the loop and the straight conductors is (A) π (B) 2π (C)  (1 /π) (D)  (1 /2 π)

Tardigrade Admin · Accepted Answer

Given that the net magnetic field at the centre

O

is zero. Therefore, magnetic field at

O

due to circular coil and straight conductor must be equal and opposite in direction.

\frac{μ _{0} l _{1}}{2 R} = \frac{μ _{0} l _{2}}{2 π ( 2 R )}

\Rightarrow \frac{l _{1}}{l _{2}} = \frac{1}{2 π} E

Q. In the diagram $I_{1}, I_{2}$ are the strength of the currents in the loop and straight conductors respectively $O A = A B = R$ . The net magnetic field at the centre $O$ is zero. Then the ratio of the currents in the loop and the straight conductors is

$π$

$2 π$

$\frac{1}{π}$

$\frac{1}{2 π}$

Given that the net magnetic field at the centre $O$ is zero. Therefore, magnetic field at $O$ due to circular coil and straight conductor must be equal and opposite in direction.
$\frac{μ _{0} l _{1}}{2 R} = \frac{μ _{0} l _{2}}{2 π ( 2 R )}$
$\Rightarrow \frac{l _{1}}{l _{2}} = \frac{1}{2 π} E$

Q. In the diagram I1​,I2​ are the strength of the currents in the loop and straight conductors respectively OA=AB=R. The net magnetic field at the centre O is zero. Then the ratio of the currents in the loop and the straight conductors is

π

2π

π1​

2π1​

Given that the net magnetic field at the centre O is zero. Therefore, magnetic field at O due to circular coil and straight conductor must be equal and opposite in direction. 2Rμ0​l1​​=2π(2R)μ0​l2​​ ⇒l2​l1​​=2π1​E

Q. In the diagram $I_{1}, I_{2}$ are the strength of the currents in the loop and straight conductors respectively $O A = A B = R$ . The net magnetic field at the centre $O$ is zero. Then the ratio of the currents in the loop and the straight conductors is

$π$

$2 π$

$\frac{1}{π}$

$\frac{1}{2 π}$