A long straight wire of radius R carries a current i . The magnetic field inside the wire at distance r(.r

Question

A long straight wire of radius R carries a current i . The magnetic field inside the wire at distance r(.r < R.) , from its centre is expressed as (A) ((μ0 i/π R2)) ⋅ r (B) ((2 μ0 i/π R2)) ⋅ r (C) ((μ0 i/2 π R2)) ⋅ r (D) ((μ0 i/2 π R)) ⋅ r

Tardigrade Admin · Accepted Answer

Using Ampere's law, we have oint overset arrow B. overset arrow d l=μ 0 ii n <img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/p-svhbkxsrpzsw.png" /> or B× 2π r=μ 0(i/π R2)π r2 ∴ B=(μ 0/2 π ).(i r/R2)

Q. A long straight wire of radius $R$ carries a current $i$ . The magnetic field inside the wire at distance $r (r < R)$ , from its centre is expressed as

$(\frac{μ _{0} i}{π R ^{2}}) \cdot r$

$(\frac{2 μ _{0} i}{π R ^{2}}) \cdot r$

$(\frac{μ _{0} i}{2 π R ^{2}}) \cdot r$

$(\frac{μ _{0} i}{2 π R}) \cdot r$

Using Ampere's law, we have
$\oint B \to . d l \to = μ_{0} i_{in}$

or $B \times 2 π r = μ_{0} \frac{i}{π R ^{2}} π r^{2}$
$∴$ $B = \frac{μ _{0}}{2 π} . \frac{i r}{R ^{2}}$

Q. A long straight wire of radius R carries a current i . The magnetic field inside the wire at distance r(r<R) , from its centre is expressed as

(πR2μ0​i​)⋅r

(πR22μ0​i​)⋅r

(2πR2μ0​i​)⋅r

(2πRμ0​i​)⋅r