(i) State and explain Ampere's circuital law. (ii) Two long straight parallel wires separated by $20\,\text{cm}$ carry $5\,\text{A}$ and $10\,\text{A}$ current respectively in the same direction. Find the magnitude and direction of the net magnetic field at a point midway between them.

(i) $\oint\vec B\cdot d\vec\ell=\mu_0 I_{enc}$. (ii) $B_P=10\,\mu\text{T}$, perpendicular to the plane of the wires.

CBSE Class 12 · 2024 · Magnetic Effects of CurrentShort Answer

(i) State and explain Ampere's circuital law.
(ii) Two long straight parallel wires separated by

20 cm

carry

5 A

and

10 A

current respectively in the same direction. Find the magnitude and direction of the net magnetic field at a point midway between them.

Answer: (i) $\oint B \cdot d ℓ = μ_{0} I_{e n c}$ .
(ii) $B_{P} = 10 μ T$ , perpendicular to the plane of the wires.

(i) \textbf{Ampere's law:} the line integral of

B

around any closed loop equals

μ_{0}

times the net current threading the loop,

\oint B \cdot d ℓ = μ_{0} I_{e n c}

. It is used to find

B

in symmetric situations. (ii) The midpoint is

0.10 m

from each wire. The two fields are opposite there (parallel currents), so they subtract:

B_{P} = \frac{μ _{0} ( 10 - 5 )}{2 π ( 0.10 )} = \frac{( 4 π \times 1 0 ^{- 7} ) ( 5 )}{2 π ( 0.10 )} = 10 μ T,

directed perpendicular to the plane of the wires (sense set by the larger,

10 A

, current).

CBSE Class 12 Board · 2024 · Subjective