Question

# A V shape bent wire is carrying current $$I$$ and ends of wire extends to infinity. If the magnetic field at $$P$$ can be written as $$K\tan { \left( \cfrac { \alpha }{ 2 } \right) }$$, then $$K$$ is

A
μ0I4πd
B
μ0I2πd
C
μ0Iπd
D
2μ0Iπd

Solution

## The correct option is B $$\cfrac { { \mu }_{ 0 }I }{ 2\pi d }$$ Magnetic field due to any one segment:$$\quad B=\cfrac { { \mu }_{ 0 }i }{ 4\pi (d\sin { \alpha } ) } \left( \cos { { 0 }^{ o } } +\cos { \left( 180-\alpha \right) } \right)$$$$=\cfrac { { \mu }_{ 0 }i }{ 4\pi (d\sin { \alpha } ) } (1-\cos { \alpha } )=\cfrac { { \mu }_{ 0 }I }{ 4\pi d } \tan { \cfrac { \alpha }{ 2 } }$$Resultant field will be$${ B }_{ net }=2B=\cfrac { { \mu }_{ 0 }I }{ 2\pi d } \tan { \cfrac { \alpha }{ 2 } } \Rightarrow K=\cfrac { { \mu }_{ 0 }I }{ 2\pi d }$$PhysicsNCERTStandard XII

Suggest Corrections

0

Similar questions
View More

Same exercise questions
View More

People also searched for
View More