First slide

Magnetic field due to current element

Question

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

Moderate

A

$\frac{B}{6}$
B

$\frac{B}{4}$
C

$\frac{B}{3}$
D

$\frac{B}{2}$

Solution

$D u e t o i n f i n t e w i r e, B = \frac{μ_{o} i}{2 π r} \Rightarrow B \propto \frac{1}{r} \Rightarrow \frac{B_{1}}{B_{2}} = \frac{r_{2}}{r_{1}} \Rightarrow \frac{B}{B_{2}} = \frac{20}{5} \Rightarrow B_{2} = \frac{B}{4}$

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