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# Time Varying Magnetic Field - Practice Questions & MCQ

Edited By admin | Updated on Sep 18, 2023 18:34 AM | #JEE Main

## Quick Facts

• Time Varying Magnetic field is considered one the most difficult concept.

• 19 Questions around this concept.

## Solve by difficulty

The flux linked with a coil at any instant t is given by $\dpi{100} \phi$ = 10t2 - 50t + 250. The induced emf (in Volts) at t = 3s is

Figure shows three regions of magnetic field, each of area A, and in each region magnitude of magnetic field decreases at a constant rate a. If  is induced electric field then value of line integral . along the given loop is equal to

A small circular loop of wire of radius a is located at the center of a much larger circular wire loop of radius b.  The two loops are in the same plane. The outer loop of radius b carries an alternating current I=Io cos (ωt).  The emf induced in the smaller inner loop is nearly :

In the figure shown a square loop PQRS of side 'a' and resistance 'r' is placed near an infinitely long wire carrying a constant current I. The sides PQ and RS are parallel to the wire. The wire and the loop are in the same plane. The loop is rotated by 180º about an axis parallel to the long wire and passing through the mid points of the side QR and PS. The total amount of charge which passes through any point of the loop during rotation is  :

## Concepts Covered - 1

Time Varying Magnetic field

As we learn Induced electric field is given by

$\varepsilon = \oint \vec{E_{in} }\cdot \vec{dl}= \frac{-d\phi }{dt}$

But using  $\phi =B.A$ so we can also write

$\varepsilon = \oint \vec{E_{in} }\cdot \vec{dl}= \frac{-d\phi }{dt}=-A\frac{dB}{dt}$

Where

$\rightarrow$ constant Area

B $\rightarrow$ Varying Magnetic field

For example-

A uniform but time-varying magnetic field B(t) exists in a circular region of radius ‘a’ and is directed into the plane of the paper as shown in the below figure, the magnitude of the induced electric field ($E_{in}$) at point P lies at a distance r from the centre of the circular region is calculated as follows.

As due to the time-varying magnetic field induced electric field will be produced whose electric field lines are concentric circular closed curves of radius r.

\begin{aligned} \ if \ \ r \leq a \\ then \ E_{in}(2 \pi r) &=\pi r^{2}\left|\frac{d B}{d t}\right| & & \\ \Rightarrow & E_{in} =\frac{r}{2}\left|\frac{d B}{d t}\right| \end{aligned}

$\begin{array}{ll}{\text { For } r>R,} \\ \\ {E_{in} *2\pi r=\pi a^{2}\left|\frac{d B}{d t}\right|} \\ \\ {\Rightarrow} {E_{in}=\frac{a^{2}}{2 r}\left|\frac{d B}{d t}\right|}\end{array}$

•  The  graph of E vs r

where E=induced electric field

## Study it with Videos

Time Varying Magnetic field

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