Two wires carrying currents 5 A and 2 A are enclosed in a circular loop as shown in the figure. Another wire carrying a current of 3 A is situated outside the loop. The value of B dl around the loop is ( μ₀ = permeability of free space, dl is the length of the element on the Amperion loop) (a) 4μ₀ (b) 2μ₀ (c) 3μ₀ (d) μ₀

Answer: (c). Ampere's law: B· dl = μ₀ Ienc; the 3 A wire outside does not count. The 5 A and 2 A currents are opposite: Ienc = 5 - 2 = 3 A. B· dl = 3μ₀ So the answer is (c).

Two wires carrying currents 5 A and 2 A are enclosed in a circular… | MHT CET 2021 (20 Sep, Shift 2)

Q35MHT CET 2021 · 20 SEP · SHIFT 2Easy

Ampere's Law, Cylinders, Solenoid & Toroid

Two wires carrying currents $5\text{ A}$ and $2\text{ A}$ are enclosed in a circular loop as shown in the figure. Another wire carrying a current of $3\text{ A}$ is situated outside the loop. The value of $\oint \vec{B}\,\vec{dl}$ around the loop is ( $\mu_0 =$ permeability of free space, $\vec{dl}$ is the length of the element on the Amperion loop)

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Answer: (c)

Ampere's law: $\oint \vec{B}\cdot d\vec{l} = \mu_0 I_{enc}$ ; the 3 A wire outside does not count.
The 5 A and 2 A currents are opposite: $I_{enc} = 5 - 2 = 3$ A.
$\oint \vec{B}\cdot d\vec{l} = 3\mu_0$
So the answer is (c).

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