A current is flowing through a thin cylindrical shell of radius $R$. If energy density in the medium, due to magnetic field, at a distance $r$ from axis of the shell is equal to $U$ then which of the following graphs is correct
A
B
C
D
Medium
Download our app for free and get started
B
b (b) When a current flows through cylindrical shell, then according to Ampere circuital law, magnetic induction inside it will be equal to zero. Hence energy density at $r < R$ is equal to zero.
Therefore, $(a)$, $(c)$ and $(d)$ are wrong.
When $r > R$, $B = \frac{{{\mu _0}i}}{{2\pi r}}$.
Since $U = \frac{{{B^2}}}{{2{\mu _0}}},$therefore, outside the shell, $U = \frac{{{\mu _0}{i^2}}}{{8{\pi ^2}{r^2}}}$. It means, just outside the shell, $U = \frac{{{\mu _0}{i^2}}}{{8{\pi ^2}{R^2}}}$ and when $r \to \infty ,\;U \to 0.$
Hence $(b)$ is correct.
Download our app
and 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.*
Mixed $H{e^ + }$ and ${O^{2 + }}$ ions (mass of $H{e^ + } = 4\,\,amu$ and that of ${O^{2 + }} = 16\,\,amu)$ beam passes a region of constant perpendicular magnetic field. If kinetic energy of all the ions is same then
A long solenoid is formed by winding $20$ $turns/cm$. The current necessary to produce a magnetic field of $20$ $milli\,tesla$ inside the solenoid will be approximately .....$A$ $(\frac{{{\mu _0}}}{{4\pi }} = {10^{ - 7}}\,tesla - metre/ampere)$
Figure $A$ and $B$ shown two long straight wires of circular cross-section ($a$ and $b$ with $a$ $<$ $b$), carrying current $I$ which is uniformly distributed across the cross-section. The magnitude of magnetic field $B$ varies with radius $r$ and can be represented as
A current $I$ flows in an infinitely long wire with cross-section in the form of a semicircular ring of radius $R$. The magnitude of the magnetic induction along its axis is
A positive charge $'q'$ of mass $'m'$ is moving along the $+ x$ axis. We wish to apply a uniform magnetic field $B$ for time $\Delta t$ so that the charge reverses its direction crossing the $y$ axis at a distance $d.$ Then
$A, B$ and $C$ are parallel conductors of equal length carrying currents $I, I$ and $2I$ respectively. Distance between $A$ and $B$ is $x$. Distance between $B$ and $C$ is also $x$. ${F_1}$ is the force exerted by $B$ on $A$ and $F_2$ is the force exerted by $B$ on $A$ choose the correct answer
If a proton, deutron and $\alpha - $ particle on being accelerated by the same potential difference enters perpendicular to the magnetic field, then the ratio of their kinetic energies is