Question

I really need help with this one .Please can you explain me with equations as well .

Answer 1

1)

magnetic field by a long current carrying wire is given as

B = ($\mu$/4$\pi$) (2I₁/r)

magnetic field at A is given as

B_A = ($\mu$/4$\pi$) (2I₁/r_A)

at A , r_A = 2 m

B_A = (10^-7) (2 x 20 /2) = 2 x 10^-6 T                inward to the page

magnetic field at B is given as

B_B = ($\mu$/4$\pi$) (2I₁/r_B)

at B , r_B = 12 m

B_B = (10^-7) (2 x 20 /12) = 0.33 x 10^-6 T inward to the page

b)

F_AC = ($\mu$/4$\pi$) (2I₁I₂ (AC)/r_A) = (10^-7) (2 x 20 x 50 x 15 / 2) = 1.5 x 10^-3 N towards left

F_BD = ($\mu$/4$\pi$) (2I₁I₂ (BD)/r_B) = (10^-7) (2 x 20 x 50 x 15 / 12) = 0.25 x 10^-3 N    towards right

C)

Net force = F = F_AC - F_BD = 1.5 x 10^-3 - 0.25 x 10^-3 = 1.25 x 10^-3    towards left

d)

dA = small area of rectangular strip = 15 dr

B = magnetic field through the strip = ($\mu$/4$\pi$) (2I₁/r)

small magnetic flux is given as

d$\phi$ = B dA = ($\mu$/4$\pi$) (2I₁ 15 dr/r)

d$\phi$ = ($\mu$/4$\pi$) (2I₁ 15) (dr/r)

integrating both side

$\phi$ = ($\mu$/4$\pi$) (2I₁ 15) (lnr_B - lnr_A) = (10^-7) (2 x 20 x 15) (ln12 - ln2) = 1.075 x 10^-4