Question

The magnetic field around a current-carrying wire is ________proportional to the current and _________proportional to the distance from the wire. If the current triples while the distance doubles, the strength of the magnetic field increases by ____times.

Answer 1

Answer:Thus, The magnetic field around a current-carrying wire is directly  proportional to the current and inversely  proportional to the distance from the wire.  If the current triples while the distance doubles, the strength of the magnetic field increases by one and half (1.5) times.

Explanation:

Magnetic field around a long current carrying wire is given by

$B=\frac{\mu _o I}{2\pi r}$

where B= magnetic field

           $\mu _o=$ permeability of free space

           I= current in the long wire and

           r= distance from the current carrying wire

Thus, The magnetic field around a current-carrying wire is directly  proportional to the current and inversely  proportional to the distance from the wire.  

Now if I'=3I and r'=2r then magnetic field B' is given by

$B'=\frac{\mu _oI'}{2\pi r'}=\frac{\mu _o3I}{2\pi 2r}=1.5B$

Thus If the current triples while the distance doubles, the strength of the magnetic field increases by one and half (1.5) times.

   

Answer 2

Directly
Inversely
1.5