An electric current passes through a long straight copper wire. At a distance 5 cm from the straight wire, the magnetic field is B. The magnetic field at 25 cm from the straight wire would be:

Question

An electric current passes through a long straight copper wire. At a distance 5 cm from the straight wire, the magnetic field is B. The magnetic field at 25 cm from the straight wire would be: (A) (B/6) (B) (B/5) (C) (B/3) (D) (B/2)

Tardigrade Admin · Accepted Answer

The magnetic field due to the straight wire at a distance r is given by B=(μ0 i/2 π r) or B propto (1/r) or (B2/B1)=(r1/r2) ∴ (B2/B)=(5/25)=(1/5) or B2=(B/5)

Q. An electric current passes through a long straight copper wire. At a distance $5 c m$ from the straight wire, the magnetic field is $B$ . The magnetic field at $25 c m$ from the straight wire would be:

$\frac{B}{6}$

$\frac{B}{5}$

$\frac{B}{3}$

$\frac{B}{2}$

The magnetic field due to the straight wire at a distance $r$ is given by
$B = \frac{μ _{0} i}{2 π r}$
or $B \propto \frac{1}{r}$ or $\frac{B _{2}}{B _{1}} = \frac{r _{1}}{r _{2}}$
$∴ \frac{B _{2}}{B} = \frac{5}{25} = \frac{1}{5}$ or $B_{2} = \frac{B}{5}$

Q. 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 25cm from the straight wire would be:

6B​

5B​

3B​

2B​