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Electromagnetic Induction

Can an induce...

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Can an induced electric field exists at a point In space, when no magnetic field is present at that point? How?

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Q. Figure shows a circular region of radius

R

in which uniform magnetic field

B

exists. The magnetic field is increasing at a rate

\frac{d B}{d t}

. The induced electric field at a distance

r

from the centre for

r < R

Q. Time varying magnetic field is present in a circular region of radius

R

. Match the properties from column-2 to column-1 using the codes given below the columns.

Column-I	Column-II
(P) An unsteady magnetic field	(1) Electric field is perpendicular to the length of rod.
(Q) Induced electric field at a point within magnetic field ( $r < R$ )	(2) $\frac{r}{2} \frac{d B}{d t}$
(R) Induced electric field at a point outside the magnetic field ( $r > R$ )	(3) $\frac{R^{2}}{2 r} \frac{d B}{d t}$
(S) If a rod is placed along the diameter of the magnetic field	(4) Induced electric field

Q. A uniform magnetic field B exists in a cylindrical region, shown dotted in figure. The magnetic field increases at a constant rate

\frac{d B}{d t}

. Consider a circle of radius r coaxial with the cylindrical region. (a) Find the magnitude of the electric field E at a point on the circumference of the circle. (b) Consider a point P on the side of the square circumscribing the circle. Show that the component of the induced electric field at P along ba is the same as the magnitude found in part (a)

Q. 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. The magnitude of the induced electric field at point P at a distance r from the centre of the circular region

Q. A plane electromagnetic wave of frequency 20 MHz travels through a space along x direction. If the electric field vector at a certain point in space is 6 V

m^{- 1}

, what is the magnetic field vector at that point?

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