Consider the two idealised systems $(i)$ a parallel plate capacitor with large plates and small separation and $(ii)$ a long solenoid of length $L >> R$, radius of cross-section. In $(i)\, E$ ideally treated as a constant between plates and zero outside. In $(ii)$ magnetic field is constant inside the solenoid and zero outside. These idealised assumptions, however, contradict fundamental laws as below
ACase $(i)$ contradicts Gauss' law for electrostatic fields
BCase $(ii)$ contradicts Gauss' law for magnetic fields
BCase $(ii)$ contradicts Gauss' law for magnetic fields
b As Gauss' law states,$\oint\limits_s {E.dS} = \frac{q}{{{\varepsilon _0}}}$ electrostatic field. It does not contradict for electrostatic fields as the electric field lines do not form continuous closed path. According to Gauss' law in magnetic field, $\oint\limits_s {E.dS} = 0$ It contradicts for magnetic field, because there is a magnetic field inside the solenoid and no field outside the solenoid carrying current but the magnetic field lines form the closed path.
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.*
An electron (mass $= 9 \times 10^{-31}\,kg$. Charge $= 1.6 \times 10^{-19}\,C$) whose kinetic energy is $7.2 \times 10^{-18}$ $joule$ is moving in a circular orbit in a magnetic field of $9 \times 10^{-5} \,weber/m^2$. The radius of the orbit is.....$cm$
An electron of charge $e$ moves in a circular orbitof radius $r$ around the nucleus at a frequency $v$. The magnetic moment associated with the orbital motion of the electron is
A long wire $AB$ is placed on a table. Another wire $PQ$ of mass $1.0\, g$ and length $50\, cm$ is set to slide on two rails $PS$ and $QR$. A current of $50\,A$ is passed through the wires. At what distance above $AB$, will the wire $PQ$ be in equilibrium.....$mm$
A straight rod of mass $m$ and length $L$ is suspended from the identical spring as shown in the figure. The spring stretched by a distance of $x_0$ due to the weight of the wire. The circuit has total resistance $R\Omega$ . When the magnetic field perpendicular to the plane of the paper is switched on, springs are observed to extend further by the same distance. The magnetic field strength is
An element $\Delta l=\Delta \mathrm{xi}$ is placed at the origin and carries a large current $\mathrm{I}=10 \mathrm{~A}$. The magnetic field on the $y$-axis at a distance of $0.5 \mathrm{~m}$ from the elements $\Delta \mathrm{x}$ of $1 \mathrm{~cm}$ length is:
Two long, straight wires carry equal currents in opposite directions as shown in figure. The separation between the wires is $5.0 \mathrm{~cm}$. The magnitude of the magnetic field at a point $P$ midway between the wires is __________$\mu \mathrm{T}$ (Given : $\mu_0=4 \pi \times 10^{-7} \mathrm{TmA}^{-1}$ )