JEE Advanced2022PhysicsMagnetic Effects of CurrentActual
Which one of the following options represents the magnetic field B → at O due to the current flowing in the given wire segments lying on the x y plane?
Options
- AB → = - μ 0 I L 3 2 + 1 4 2 π k ^
- BB → = - μ 0 I L 3 2 + 1 2 2 π k ^
- CB → = - μ 0 I L 1 + 1 4 2 π k ^
- DB → = - μ 0 I L 1 + 1 4 π k ^
Correct answer
C. B → = - μ 0 I L 1 + 1 4 2 π k ^
Step-by-step solution
Magnetic field due to a straight wire will be zero if the line of the wire passes through the point of interest. Therefore, In the above figure, B B C + B D E + B F G = 0 Therefore, B → net   = B → A B + B → C D   + B → E F Magnetic field due to a finite wire is given by, B = μ 0 I 4 π d sin α + sin β Using above formula, B → A B = μ 0 I 4 π L × 1 2 - k ^ Magnetic field due to a circular arc is, B = μ 0 I 2 R × θ 2 π Ther