The magnetic field intensity at the point O of a loop with current i, whose shape is illustrated below is

Question

The magnetic field intensity at the point O of a loop with current i, whose shape is illustrated below is (A) (μ0 i/4 π)[(3 π/2 a)+(√2/b)] (B) (μ0 i/4 π2)[(2/a)+b] (C) (μ0 i/2 π)[(1/a)+(1/b)] (D) (μ0 i/4 π)[(1/a)+(1/b)]

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/23fe448429e258ee7331ea09078db2a3-.png" /> vecB due to square part :- vecB due to side O A and O C will be zero at point O vecB due to side A B and B C will be equal so vecB1=2[(μ0 i/4 π b)( sin 45°+0)]=(μ0 i/2 √2 π b) otimes vecB due to circular part vecB2=(μ0 i/2 a)[(((3 π/2))/2 π)]=(3 μ0 i/8 a) otimes vecB text net = vecB1+ vecB2=μ0[(3/8 a)+(1/2 √2 π b)] =(μ0 i/4 π)[(3 π/2 a)+(√2/b)]

Q. The magnetic field intensity at the point $O$ of a loop with current $i$ , whose shape is illustrated below is

$\frac{μ _{0} i}{4 π} [\frac{3 π}{2 a} + \frac{2}{b}]$

$\frac{μ _{0} i}{4 π ^{2}} [\frac{2}{a} + b]$

$\frac{μ _{0} i}{2 π} [\frac{1}{a} + \frac{1}{b}]$

$\frac{μ _{0} i}{4 π} [\frac{1}{a} + \frac{1}{b}]$

Q. The magnetic field intensity at the point O of a loop with current i, whose shape is illustrated below is

4πμ0​i​[2a3π​+b2​​]

4π2μ0​i​[a2​+b]

2πμ0​i​[a1​+b1​]

4πμ0​i​[a1​+b1​]

Q. The magnetic field intensity at the point $O$ of a loop with current $i$ , whose shape is illustrated below is

$\frac{μ _{0} i}{4 π} [\frac{3 π}{2 a} + \frac{2}{b}]$

$\frac{μ _{0} i}{4 π ^{2}} [\frac{2}{a} + b]$

$\frac{μ _{0} i}{2 π} [\frac{1}{a} + \frac{1}{b}]$

$\frac{μ _{0} i}{4 π} [\frac{1}{a} + \frac{1}{b}]$