NEET2016PhysicsMagnetic Effects of CurrentActual
The magnetic field at the centre O of the arc shown in the figure is
Options
- A2 I( 2 + ) 10⁻⁷ r
- B2 I ( 2 + 4 ) 10⁻⁷ r
- CI( 2 + ) 10⁻⁷ r
- DI ( 2 + 4 ) 10⁻⁷ r
Correct answer
B. 2 I ( 2 + 4 ) 10⁻⁷ r
Step-by-step solution
Here, a= r 2 Magnetic field at point O due to A B is B₁= ₀ 4 I a = ₀ I 4 (r / 2 ) Magnetic field at point O due to B C D is B₂= ₀ I 4 r ( 2 ) Magnetic field at point O due to D E is B₃= ₀ I 4 a = ₀ I 4 (r / 2 ) Resultant magnetic field at point O is aligned B & =B₁+B₂+B₃ & = ₀ I 4 (r / 2 ) + ₀ I 4 r ( 2 )+ ₀ I 4 (r / 2 ) & = ₀ I 4 r ( 2 + 2 + 2 )= ₀ I 4 r (2 2 + 2 ) & = ₀ I I 4 r ( 2 + 4 ) & = 10⁻⁷ 2 I r ( 2 + 4 ) [ ₀ 4 =10⁻⁷ ] aligned