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

Question

An electric current passes through a long straight wire. At a distance 5 cm from the wire, the magnetic field is B. The field at 20 cm from the wire would be (A) 2B (B) B/4 (C) B/2 (D) B

Tardigrade Admin · Accepted Answer

For a long straight wire, the magnetic field

B = \frac{μ _{0} 2 I}{4 π r}

When

r = 5 c m

∴ B = \frac{μ _{0} 2 I}{4 π ( 5 )} .... (i)

Similarly, when

r = 20 c m

B^{'} = \frac{μ _{0} 2 I}{4 π ( 20 )} ... (ii)

From Eqs. (i) and (ii), we get

B^{'} = \frac{B}{4}

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

2B

B/4

B/2

B

For a long straight wire, the magnetic field B=4πrμ0​2I​ When r=5cm ∴B=4π(5)μ0​2I​....(i) Similarly, when r=20cm B′=4π(20)μ0​2I​...(ii) From Eqs. (i) and (ii), we get B′=4B​

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

For a long straight wire, the magnetic field
$B = \frac{μ _{0} 2 I}{4 π r}$

When $r = 5 c m$
$∴ B = \frac{μ _{0} 2 I}{4 π ( 5 )} .... (i)$
Similarly, when $r = 20 c m$
$B^{'} = \frac{μ _{0} 2 I}{4 π ( 20 )} ... (ii)$
From Eqs. (i) and (ii), we get
$B^{'} = \frac{B}{4}$