Four circular loops of radii 1 ; CM,2 ; CM,3 | vedclass

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(D) The magnetic field $B$ at the center of a circular current-carrying loop is given by the formula $B = \frac{\mu_0 I}{2R}$,where $\mu_0$ is the per

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$1 \; CM$ radius

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(D) The magnetic field $B$ at the center of a circular current-carrying loop is given by the formula $B = \frac{\mu_0 I}{2R}$,where $\mu_0$ is the permeability of free space,$I$ is the current,and $R$ is the radius of the loop.From this formula,it is clear that the magnetic field $B$ is inversely proportional to the radius $R$ $(B \propto \frac{1}{R})$.Since the current $I$ is the same for all loops,the loop with the smallest radius will have the strongest magnetic field at its center.Comparing the given radii ($1 \; CM$,$2 \; CM$,$3 \; CM$,and $4 \; CM$),the smallest radius is $1 \; CM$.Therefore,the loop with a radius of $1 \; CM$ will have the strongest magnetic field at its center.

Four circular loops of radii $1 \; CM$,$2 \; CM$,$3 \; CM$,and $4 \; CM$ carry the same electric current. At the center of which loop will the magnetic field be the strongest?

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