Two concentric and coplanar circular loops P and Q have their radii in the ratio 2:3. Loop Q carries a current 9 A in the anticlockwise direction. For the magnetic field to be zero at the common centre, loop P must carry ______.

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Two concentric and coplanar circular loops P and Q have their radii in the ratio 2:3. Loop Q carries a current 9 A in the anticlockwise direction. For the magnetic field to be zero at the common centre, loop P must carry 6 A in the clockwise direction. Explanation: Given: The ratio of the radius of the loops P and Q = 2:3 Current in the loop Q = 9 A in (anticlockwise direction) To Find: The current in loop P for which the magnetic field at the common centre becomes zero. $\Rightarrow$ The intensity of the magnetic field (B) at the centre of a circular current-carrying coil is given by the formula: Magnetic Field (B) = (μ_0i)/(2R) • Where 'i' is the current flowing through the circular coil. • Here 'R' is the radius of the circular coil. • 'μ0' is a constant known as the permeability constant of free space. $\Rightarrow$ The direction of the magnetic field due to the circular current-carrying coil is given by the right-hand thumb rule. According to this law, if we curl our right-hand palm around the current-carrying loop with fingers pointing in the direction of the current flow, then the direction of our right-hand thumb will give us the direction of the Magnetic field. $\Rightarrow$ In the given question, the current in loop Q is flowing in the anticlockwise direction. Therefore for the resultant magnetic field to be zero at the common centre, the current in the loop P must flow in the clockwise direction. Let the magnetic field due to the loop P be 'B1' Let the magnetic field due to the loop Q be 'B2' Let the current through the loop P be 'i1' The ratio of the radius of the loops P and Q is R1:R2 is equal to 2:3. $\Rightarrow$ The magnetic field 'B1' due to the current-carrying loop P is given by: B1 = (μ_0i_1)/(2R_1) – Equation (i) $\Rightarrow$ The magnetic field 'B2' due to the current-carrying loop Q is given by: B2 = (μ_0i_2)/(2R_2) – Equation (ii) $\Rightarrow$ Equating the equations (i) and (ii): ∵ B1 = B2 $\therefore$ `(μ_0i_1)/(2R_1) = (μ_0i_2)/(2R_2) $\therefore$ i_1/i_2 = R_1/R_2 $\therefore$ i_1 = $\frac{2}{3}$ xx i_2 $\therefore$ i_1 = $\frac{2}{3}$ xx 9` $\therefore$ i1 = 6 Ampere Therefore for the magnetic field to be zero at the common centre, the loop P must carry​ a current of 6 Ampere in the clockwise direction.

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