Write equation of magnetic field due to a circular current carrying loop at a point on the axis of the loop. Give its special cases.
Write equation of magnetic field due to a circular current carrying loop at a point on the axis of the loop. Give its special cases.
Magnetic field $\overrightarrow{\mathrm{B}}$ due to I current carrying wire with $\mathrm{R}$ radius at a $x$ distance is given by, $B=\frac{\mu_{0} I R^{2}}{2\left(x^{2}+R^{2}\right)^{3 / 2}}$
Case $1:$
When number of turns are $\mathrm{N}$, then magnetic field is $\mathrm{B}=\frac{\mu_{0} \mathrm{NIR}^{2}}{2\left(x^{2}+\mathrm{R}^{2}\right)^{3 / 2}}$
Case $2:$
Magnetic field at centre with $\mathrm{N}$ turn $\mathrm{B}=\frac{\mu_{0} \mathrm{NI}}{2 \mathrm{R}}$
Case $3$ :
When $x>>\mathrm{R}$, then $\mathrm{B}=\frac{\mu_{0} \mathrm{NIR}^{2}}{2 x^{3}}$
Case $4$ :
At $x=\mathrm{R}$ distance from centre,
$B=\frac{\mu_{0} N I R^{2}}{2\left(R^{2}+R^{2}\right)^{3 / 2}}=\frac{\mu_{0} N I}{2^{5 / 2} R}$
Similar Questions
Two infinitely long wires each carrying current $I$ along the same direction are made into the geometry as shown in the figure below. The magnetic field at the point $P$ is
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A current loop $ABCD$ is held fixed on the plane of the paper as shown in the figure. The arcs $ BC$ (radius $= b$) and $DA $ (radius $= a$) of the loop are joined by two straight wires $AB $ and $CD$. A steady current $I$ is flowing in the loop. Angle made by $AB$ and $CD$ at the origin $O$ is $30^o $. Another straight thin wire with steady current $I_1$ flowing out of the plane of the paper is kept at the origin.
The magnitude of the magnetic field $(B)$ due to the loop $ABCD$ at the origin $(O)$ is :
A current loop $ABCD$ is held fixed on the plane of the paper as shown in the figure. The arcs $ BC$ (radius $= b$) and $DA $ (radius $= a$) of the loop are joined by two straight wires $AB $ and $CD$. A steady current $I$ is flowing in the loop. Angle made by $AB$ and $CD$ at the origin $O$ is $30^o $. Another straight thin wire with steady current $I_1$ flowing out of the plane of the paper is kept at the origin.
The magnitude of the magnetic field $(B)$ due to the loop $ABCD$ at the origin $(O)$ is :
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Acharged particle enters a uniform magnetic field perpendicular to its initial direction travelling in air. The path of the particle is seen to follow the path in figure. Which of statements $1-3$ is/are correct?
$[1]$ The magnetic field strength may have been increased while the particle was travelling in air
$[2]$ The particle lost energy by ionising the air
$[3]$ The particle lost charge by ionising the air
Acharged particle enters a uniform magnetic field perpendicular to its initial direction travelling in air. The path of the particle is seen to follow the path in figure. Which of statements $1-3$ is/are correct?
$[1]$ The magnetic field strength may have been increased while the particle was travelling in air
$[2]$ The particle lost energy by ionising the air
$[3]$ The particle lost charge by ionising the air