Induced Electric Field

A thin non-conducting ring of mass $m$ and radius $a$ currying a charge $q$ can rotate freely about its own axis which is vertical. At the initial moment the ring was at rest in horizontal position and no magnetic field was present. At instant $t=0$, a uniform magnetic field is switched on which is vertically downward and increases with time according to the law $B=B_{0}t$. Neglecting magnetism induced due to rotational motion of ring.

Angular acceleration of the ring is:

A non-conducting ring of mass $m$ and radius $R$ has a charge $Q$ uniformly distributed over its circumference. The ring is placed on a rough horizontal surface such that the plane of the ring is parallel to the surface. A vertical magnetic field $B=B_0{t}^2$ $\mathrm{tesla}$ is switched on. After $2$ second from switching on the magnetic field, the ring is just about to rotate about a vertical axis through its centre. Find friction coefficient $\mu$ between the ring and the surface. [Given that $\left.mg=B_{0}QR\right]$ (All physical quantities are in $\mathrm{S}.\mathrm{I}.$ unit)

A ring of mass $4 \mathrm{kg}$ is uniformly charged with a linear charge density $\mathrm{\lambda }=4\mathrm{ }\mathrm{C} {\mathrm{m}}^{-1}$ and kept on a rough horizontal surface with a friction coefficient of $\mathrm{\mu }=\frac{\mathrm{\pi }}{4}$. A time-varying magnetic field $B\mathit{=}{B}_{\mathit{0}}{t}^{\mathit{2}}$ is applied in a circular region of radius $a$ $(a<r)$ perpendicular to the plane of the ring as shown in the figure. Find out the time (in seconds) when the ring just starts to rotate on the surface. (take $a=5 \mathrm{cm}$, $g=10\mathrm{ }\mathrm{m} {\mathrm{s}}^{-2}$ and $B_{\mathit{0}}=125 \mathrm{T} {\mathrm{s}}^{-2}$ )

The circular wire in figure below encircles solenoid in which the magnetic flux is increasing at a constant rate out of the plane of the page.

The clockwise emf around the circular loop is ${\epsilon }_0.$ By definition a voltammeter measures the voltage difference between the two points given
by $V_b-V_a=-{\int }_a^b\overrightarrow{E}·\mathrm{d}\overrightarrow{s}.$ We assume that $a$ and $b$are infinitesimally close to each other. The values of $V_b-V_a$ along the path $1$ and $V_a-V_b$ along the path $2,$ respectively are

A uniform but time-varying magnetic field $B\left(t\right)$ Exists in a circular region of radius $\text{'}a\text{'}$ And is directed into the plane of the paper, as shown. The magnitude of the induced electric field at point $P$ At a distance $r$ From the centre of the circular region

Figure shows a uniform magnetic field $\mathrm{B}$ confined to a cylindrical volume and increasing at a constant rate. The instantaneous acceleration experienced by an electron placed at $\mathrm{P}$ is-

A solenoid of radius $R$ and length $L$ has a current $\mathrm{I}={\mathrm{I}}_0 \cos \omega \mathrm{t}.$ The value of induced electric field at a distance of $r$ outside the solenoid, is:

A uniform but time varying magnetic field $B=2t^3+24t$ is represent in a cylindrical region of radius $R=2.5 \mathrm{cm}$ as shown in fig.

The force on an electron at $P$ at $t=2\sec .$ is

Figure shows an irregular shapped wire $AB$ moving with velocity $v.$ Find the emf induced in the wire :-

As shown in the above figure, there is a uniform magnetic induction $B$ parallel to the axis of a cylindrical space of radius $R$. Plot the graph between the induced electric field and distance $r$ from the axis of the cylinder, if it is known that the rate of change of magnetic induction is constant.

As shown in the above figure, consider a closed-loop held in a magnetic field. The change in the magnetic flux linked with the loop induces a voltage $V$ in the loop. Now, find the work done in taking a charge $Q$ over a complete loop:

Consider a cylindrical region of radius $R$, where a uniform magnetic field of induction $B$ is confined. At point $P$, a negative charge of magnitude $e$ is placed. Find the acceleration of the charge, if $\frac{\mathrm{d}B}{\mathrm{d}t}=C$, where $C$ is a constant.

As shown in the above figure, a loop surrounds three regions of the magnetic field where the magnitude of the magnetic field is decreasing at a constant rate $\alpha$. Take the area of each region as $A$. Now find the $\oint \overrightarrow{\mathit{E}}\mathit{.}\overrightarrow{\mathit{d}\mathit{l}}$ along the given loop, where $\overrightarrow{\mathit{E}}$ is the induced electric field.

Consider the uniform magnetic field of magnitude $0.01 \mathrm{T}$ directed perpendicularly to the plane of a conducting ring of the radius $1 \mathrm{m}$. If the ring is oscillating with a frequency of $0.1 \mathrm{kHz}$, then find the induced electric field.

Consider a $q$ charged ring of radius $b$ and mass $m$ in $x\mathit{-}y$ plane with its centre at the origin. There is a magnetic field $B$ which is confined to a region $r\le a$ and points out of the paper. Here, $r=0$ is origin and $a<b$. If this magnetic field is brought to zero in time $\text{Δ}t$, then find the angular velocity of the ring after the field vanishes,

A thin non-conducting ring of mass $m$ and radius $a$ carrying a charge $q$ can rotate freely about its own axis which is vertical. At the initial moment the ring was at rest in horizontal position and no magnetic field was present. At instant $t=0$, a uniform magnetic field is switched on which is vertically downward and increases with time according to the law $B=B_{0}t$. Neglecting magnetism induced due to rotational motion of ring.

Angular acceleration of the ring is:

A parabola $\mathrm{y}=\mathrm{k}{\mathrm{x}}^2$ shaped wire is placed in aperpendicular uniform magnetic field of induction B. At $\mathrm{t}\mathrm{ }=\mathrm{ }0$, wire starts moving from the vertex O with a constant acceleration linearly as shown in figure.Then emf induced in the loop will be-

A uniform disc of radius $r$ and mass $\mathrm{m}$ is charged uniformly with the charge $q$. This disc is placed flat on a rough horizontal surface having coefficient of friction $\mu$. Find the time in second after which the disc begins to rotate when a uniform magnetic field is present in a circular region of radius a $(>r)$ but varying as $k{t}^3$ as shown in figure. (Given $r=1 \mathrm{m}, m=18 \mathrm{kg}, \mu =0.1, k=4, g=10 \mathrm{m} {\mathrm{s}}^{-2}$). $$$$

There is a non conducting ring of radius $R$ and mass m having charge $q$ uniformly distributed over its circumference. It is placed on a rough horizontal surface. A vertical time varying uniform magnetic field $B=4t^2$ is switched on at time $t=0$. The coefficient of friction between the ring and the table, if the ring starts rotating at $t=1\sec$, is

A uniform but time-varying magnetic field $B\left(t\right)$ directed into the plane of the paper exists in a circular region of radius $a$ as shown. The magnitude of the induced electric field at point $P\left(\text{outside circular region}\right)$ which is at a distance $r$ from the centre of the circular region
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