The magnetic field at the centre of a circular current carrying-conductor of radius $r$ is $B_c$. The magnetic field on its axis at a distance $r$ from the centre is $B_a$. The value of $B_c : B_a$ will be :-
Diffcult
Download our app for free and get started
Magnetic field at centre of currentcarrying coil,
$B_{c}=\frac{\mu_{0} I}{2 r}.........(i)$
Magnetic field at axial point due to a current-carrying coil at distance of $r$
$\mathrm{d}=r$
$\mathrm{B}=\frac{\mu_{0} \operatorname{Ir}^{2}}{2\left(\mathrm{r}^{2}+\mathrm{d}^{2}\right)^{3 / 2}}$
$\Rightarrow \mathrm{B}_{\mathrm{a}}=\frac{\mathrm{\mu}_{0} \mathrm{Ir}^{2}}{2\left(2 \mathrm{r}^{2}\right)^{3 / 2}}.........(ii)$
Now, $\frac{\mathrm{B}_{\mathrm{c}}}{\mathrm{B}_{\mathrm{a}}}=\frac{\mu_{0} \mathrm{I}}{2 \mathrm{r}} \times \frac{2\left(2 \mathrm{r}^{2}\right)^{3 / 2}}{\mu_{0} \mathrm{Ir}^{2}}=2 \sqrt{2}$
$\mathrm{B}_{\mathrm{c}}: \mathrm{B}_{\mathrm{a}}=2 \sqrt{2}: 1$
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1Two circular coils $P$ and $Q$of $100$ turns each have same radius of $\pi \mathrm{cm}$. The currents in $\mathrm{P}$ and $\mathrm{R}$ are $1 \mathrm{~A}$ and $2 \mathrm{~A}$ respectively. $\mathrm{P}$ and $\mathrm{Q}$ are placed with their planes mutually perpendicular with their centers coincide. The resultant magnetic field induction at the center of the coils is $\sqrt{\mathrm{x}} \mathrm{mT}$, where X=___.View Solution
$\left[\text { Use } \mu_0=4 \pi \times 10^{-7} \mathrm{TmA}^{-1}\right]$
- 2A particle of charge $ - 16 \times {10^{ - 18}}$ $coulomb$ moving with velocity $10\,\,m{s^{ - 1}}$ along the $x$-axis enters a region where a magnetic field of induction $B$ is along the $y$-axis, and an electric field of magnitude ${10^4}\,\,V/m$ is along the negative $z$-axis. If the charged particle continues moving along the $x$-axis, the magnitude of $B$ isView Solution
- 3A proton, an electron, and a Helium nucleus, have the same energy. They are in circular orbitals in a plane due to magnetic field perpendicular to the plane. Let $r_p, r_e$ and $r_{He}$ be their respective radii, thenView Solution
- 4Figure represents four positions of a current carrying coil is a magnetic field directed towards right. $\hat n$ represent the direction of area of vector of the coil. The correct order of potential energy isView Solution
- 5A particle of mass $m$ and charge $q$ enters a region of magnetic field (as shown) with speed $v$. There is a region in which the magnetic field is absent, as shown. The particle after entering the region collides elas tically with a rigid wall. Time after which the velocity of particle becomes anti parallel to its initial velocity isView Solution
- 6A particle of mass $m$ and charge $q$ moves with a constant velocity $v$ along the positive $x$ direction. It enters a region containing a uniform magnetic field $B$ directed along the negative $z$ direction, extending from $x = a$ to $x = b$. The minimum value of $v$ required so that the particle can just enter the region $x > b$ isView Solution
- 7View SolutionThe magnetic field near a current carrying conductor is given by
- 8What is the magnetic field at a distance $R$ from a coil of radius $r$ carrying current $I$ ?View Solution
- 9If wire of length $L$ form a loop of radius $R$ and have $n$ turn. Find magnetic field at centre of loop if current flowing in loop is $I$View Solution
- 10View SolutionThe direction of magnetic force on the electron as shown in the diagram is along
