Question

Find the magnitude of magnetic field at point O. The length of AC, AB, BD, CD are equal.(where I it's the current)

Answer 1

Refer to the attachments ,

here is a two cases arrive 1st when we split the current into two part than B will be zero on the center.

Now ,

We know,  $a = l /2$

θ₁ = θ₂ = π /4

Now magnetic field ,

$\vec_B$ = μ₀ i / 4π a ( sin 45° + sin 45° ) $\hat_k$

=  ( μ₀ i / 4 π a) × ( 2 /√2 )$\hat_k$

$\vec_B_2$= (μ₀i / 4πa) × (2 /√2)$\hat_k$

a = l / 2

$\vec_B_n_e_t$ = 4μ₀i/ πl × ( 1/√2)$\hat_k$

Hence it is the magnitude of the magnetic field.

Hope it helps . :-)

Answer 2

Answer:

recommend the pic attached