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MHT CET202520 Apr 2025Evening ShiftPhysicsMagnetic Effects of CurrentActual

A current ' I ' is flowing in a conductor PQRST as shown in figure. The radius of curved path QRS is ' R ' and length of straight portion PQ and ST is very large. The magnetic field at the centre [O] of the curved part is ( ₀= permeability of free space)

Options

  1. A₀ i 4 r ( 3 2 +1 )(- k )
  2. B₀ i 4 r ( 3 2 +1 ) k
  3. C₀ i 4 r [ 3 2 -1 ](- k )
  4. D₀ i 4 r [ 3 2 -1 ] k

Correct answer

B. ₀ i 4 r ( 3 2 +1 ) k

Step-by-step solution

The total magnetic field at point O is found by summing contributions from all conductor segments. The circular arc QRS contributes B_ QRS = ₀ I 4 r ( 3 2 ) (- k ) using the formula for a current-carrying arc with subtended angle 270^ . The straight segment PQ contributes B_ PQ = 0 since point O lies along its axis, making d l r throughout. The semi-infinite segment ST contributes B_ ST = ₀ I 4 r (+ k ) at perpendicular distance r . The vector sum gives B_ total = ₀ I 4 r [- 3 2 + 1 ] k = ₀ I 4 r [1 - 3 2 ] k This

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