The magnetic field at the centre of a circular coil of radius $r$ is $\pi $ times that due to a long straight wire at a distance $r$ from it, for equal currents. Figure here shows three cases : in all cases the circular part has radius $r$ and straight ones are infinitely long. For same current the $B$ field at the centre $P$ in cases $1$, $2$, $ 3$ have the ratio
The magnetic field at the centre of a circular coil of radius $r$ is $\pi $ times that due to a long straight wire at a distance $r$ from it, for equal currents. Figure here shows three cases : in all cases the circular part has radius $r$ and straight ones are infinitely long. For same current the $B$ field at the centre $P$ in cases $1$, $2$, $ 3$ have the ratio
- A
$\left( { - \frac{\pi }{2}} \right):\left( {\frac{\pi }{2}} \right):\left( {\frac{{3\pi }}{4} - \frac{1}{2}} \right)$
- B
$\left( { - \frac{\pi }{2} + 1} \right):\left( {\frac{\pi }{2} + 1} \right):\left( {\frac{{3\pi }}{4} + \frac{1}{2}} \right)$
- C
$ - \frac{\pi }{2}:\frac{\pi }{2}:3\frac{\pi }{4}$
- D
$\left( { - \frac{\pi }{2} - 1} \right):\left( {\frac{\pi }{2} - \frac{1}{4}} \right):\left( {\frac{{3\pi }}{4} + \frac{1}{2}} \right)$
Similar Questions
The magnetic field at the origin due to a current element $i\,\overrightarrow {dl} $ placed at position $\vec r$ is
$(i)\,\,\left( {\frac{{{\mu _0}i}}{{4\pi }}} \right)\left( {\frac{{d\vec l\, \times \,\vec r}}{{{r^3}}}} \right)$
$(ii)\,\, - \left( {\frac{{{\mu _0}i}}{{4\pi }}} \right)\left( {\frac{{d\vec l\, \times \,\vec r}}{{{r^3}}}} \right)$
$(iii)\,\left( {\frac{{{\mu _0}i}}{{4\pi }}} \right)\left( {\frac{{\,\vec r \times d\vec l}}{{{r^3}}}} \right)$
$(iv)\, - \left( {\frac{{{\mu _0}i}}{{4\pi }}} \right)\left( {\frac{{\,\vec r \times d\vec l}}{{{r^3}}}} \right)$
The magnetic field at the origin due to a current element $i\,\overrightarrow {dl} $ placed at position $\vec r$ is
$(i)\,\,\left( {\frac{{{\mu _0}i}}{{4\pi }}} \right)\left( {\frac{{d\vec l\, \times \,\vec r}}{{{r^3}}}} \right)$
$(ii)\,\, - \left( {\frac{{{\mu _0}i}}{{4\pi }}} \right)\left( {\frac{{d\vec l\, \times \,\vec r}}{{{r^3}}}} \right)$
$(iii)\,\left( {\frac{{{\mu _0}i}}{{4\pi }}} \right)\left( {\frac{{\,\vec r \times d\vec l}}{{{r^3}}}} \right)$
$(iv)\, - \left( {\frac{{{\mu _0}i}}{{4\pi }}} \right)\left( {\frac{{\,\vec r \times d\vec l}}{{{r^3}}}} \right)$
A straight conductor carrying current $i$ splits into two parts as shown in the figure. The radius of the circular loop is $R$. The total magnetic field at the centre $P$ of the loop is
A straight conductor carrying current $i$ splits into two parts as shown in the figure. The radius of the circular loop is $R$. The total magnetic field at the centre $P$ of the loop is
- [NEET 2019]
A circular coil ‘$A$’ has a radius $R$ and the current flowing through it is $I$. Another circular coil ‘$B$’ has a radius $2R$ and if $2I$ is the current flowing through it, then the magnetic fields at the centre of the circular coil are in the ratio of (i.e.${B_A}$ to ${B_B}$)
A circular coil ‘$A$’ has a radius $R$ and the current flowing through it is $I$. Another circular coil ‘$B$’ has a radius $2R$ and if $2I$ is the current flowing through it, then the magnetic fields at the centre of the circular coil are in the ratio of (i.e.${B_A}$ to ${B_B}$)
- [AIEEE 2002]
The magnetic field due to a current carrying square loop of side a at a point located symmetrically at a distance of $a/2$ from its centre (as shown is)
The magnetic field due to a current carrying square loop of side a at a point located symmetrically at a distance of $a/2$ from its centre (as shown is)
A coil of $50\, turns$ and $4\,cm$ radius carries $2\,A$ current then magnetic field at its centre is......$mT$
A coil of $50\, turns$ and $4\,cm$ radius carries $2\,A$ current then magnetic field at its centre is......$mT$