question_answer

An electric current passes through a long straight wire. At a distance 5 cm from the wire, the magnetic field is B. The field at 20 cm from the wire would be

A) 2 B                                         

B) B/4

C) B/2                                        

D) B

Correct Answer: B

Solution :

For a long straight wire, the magnetic field \[B=\frac{{{\mu }_{0}}2I}{4\pi r}\] When \[r=5\,cm\] \[\therefore \]     \[B=\frac{{{\mu }_{0}}2I}{4\pi (5)}\]                     ?(i)                                        Similarly, when r = 20 cm       \[B'=\frac{{{\mu }_{0}}2I}{4\pi (20)}\]               ?(ii) From Eqs. (i) and (ii), we get \[B'=\frac{B}{4}\]