Question

Draw the pattern of magnetic field lines through and around a current-carrying wire. Make the direction of (i) electric current in the wire (ii) magnetic field lines.
How would the strength of magnetic field due to current, carrying loop be affected if
(a) radius of the loop is reduced to half its original value?
(b) strength of current through the wire is doubled?

Answer 1

$B=\frac{{\mu }_{0}I}{4\pi R}[\cos {\theta }_1+\cos {\theta }_2]$
If radius halved
$=\frac{{\mu }_{0}I}{4\pi \left(\frac{R}{2}\right)}[\cos {\theta }_1+\cos {\theta }_2]$
$=2B$
If current doubled,
$B^{\prime }=2B$
${\mu }_0\to$ magnetic permeability of vaccum
$I\to current$
$R\to radius$
$Q\to angle$ substended by wire.