Question

plz help...❤❤❤​ it's urgent for 15 points with explanation

Answer 1

Answer:

Hope it helps....................

Answer 2

▶ Solution :

Given :

✏ Two parallel wires carrying equal currents in opposite directions and placed at x = ±a (parallel to y-axis).

✏ Magnetic field at origin = B1

✏ Magnetic field at P(2a,0,0) = B2

To Find :

▪ Ratio of B1 and B2

Formula :

☞ Magnetic field due to an infinitely long straight conductor is given by

$\underline{\boxed{\bf{\red{B=\dfrac{\mu_o I}{2\pi x}}}}}$

Calculation :

☞ Calculation of B1

$\implies\bf\:B_1=B_A+B_B\\ \\ \implies\sf\:B_1=\dfrac{\mu_o I}{2a}(\hat{k})+\dfrac{\mu_o I}{2a}(\hat{k})\\ \\ \implies\bf\:B_1=\dfrac{\mu_o I}{a}(\hat{k})$

☞ Calculation of B2

$\implies\bf\:B_2=B_A+B_B\\ \\ \implies\sf\:B_2=\dfrac{\mu_o I}{2(3a)}(\hat{k})+\dfrac{\mu_o I}{2a}(-\hat{k})\\ \\ \implies\sf\:B_2=\dfrac{\mu_o I}{6a}(\hat{k})-\dfrac{\mu_o I}{2a}(\hat{k})\\ \\ \implies\sf\:B_2=\dfrac{\mu_o I-3\mu_o I}{6a}(\hat{k})\\ \\ \implies\bf\:B_2=-\dfrac{\mu_o I}{3a}(\hat{k})$

☞ Taking ratio of both

$\implies\sf\:\dfrac{B_1}{B_2}=\dfrac{\mu_o I}{a}\times \dfrac{-3a}{\mu_o I}\\ \\ \implies\boxed{\bf{\purple{B_1:B_2=-3:1}}}$

✒ Option-A) is correct.