Home
Class 12
PHYSICS
The magnetic field at all points within ...

The magnetic field at all points within the cyllindrical region whose cross section is indicated in the accompanying Figure starts increasing at a constant rate `alpha`. `T//s`. find the magnitud of electric field as a function of `r`, the distance from the geometric centre of the region.

Text Solution

Verified by Experts

Case-1:- For `r lt R`
Case-2:- r=R
`E.2pir= -A(dB)/(dt)" "E.2pi R= -pi R^(2)(dB)/(dt)`
`E.2pi r= -pi r^(2)(dB)/(dt)" "E= -(R)/(2)(dB)/(dt)`
`E= -(r)/(2)(dB)/(dt)=-(r)/(2)alpha" "E= -(Ralpha)/(2)`
`E alpha R`
Case-3:- `r gt R`
`E.2pi r= -piR^(2)(dB)/(dt)`
`e= -(R^(2))/(2r)(dB)/(dt)`
`E= -(R^(2))/(2r)alpha`
`E_("out") alpha (1)/(r)`
Promotional Banner

Topper's Solved these Questions

  • ELECTROMAGNETIC INDUCTION

    AAKASH SERIES|Exercise EXERCISE-IA|58 Videos

  • ELECTROMAGNETIC INDUCTION

    AAKASH SERIES|Exercise EXERCISE-IB|18 Videos

  • ELECTRIC FIELD AND POTENTIAL

    AAKASH SERIES|Exercise PROBLEMS (LEVEL-II)|26 Videos

  • ELECTROMAGNETIC WAVES

    AAKASH SERIES|Exercise EXERCISE -II|22 Videos

Similar Questions

Explore conceptually related problems

The magnetic field within cylindrical region whose cross - section is indicated starts increasing at a constant rate alpha tesla/sec . The graph showing the variation of induced field with distance r from the axis of cylinder is :

The magnetic field B at all points within a circular region of the radius R is uniform space and directed into the plane of the page in figure. If the magnetic field is increasing at a rate dB//dt what are the magnitude and direction of the force on as stationary positive point charge q located at points a,b, c ? (Point a is a distance r above the centre of the region, point b is a distance r to the right to the centre and point c is at the centre of the region).

A uniform magentic field of induction B is confined in a cyclinderical region of radius R . If the field is incresing at a constant rate of (dB)/(dt)= alpha T//s , then the intensity of the electric field induced at point P , distant r from the axis as shown in the figure is proportional to :

A non-conducting solid sphere of radius R, has a uniform charge density. The graph representing variation of magnitude of electric field (E) as a function of distance (x) from the centre of the sphere is

A cylindrical space of radius R is filled with a uniform magnetic induction parallel to the axis of the cylinder. If B charges at a constant rate, the graph showin the variation of induced electric field with distance r from the axis of cylinder is

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

A uniform but time varying magnetic field is present in a circular region of radius R. The magnetic field is perpendicular and into the plane of the loop and the magnitude of field is increasing at a constant rate alpha . There is a straight conducting rod of length 2R placed as shown in figure. The magnitude of induced emf across the rod is

Figure shows a circular region of radius R in which uniform magnetic field B exists. The magnetic field is increasing at a rate (dB)/(dt) . The induced electric field at a distance r from the centre for r lt R is

A uniform but time varying magnetic field B(t) exist 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 form the centre of the circular region.

A cylinderical conductor of radius R is carrying constant current. The plot of the magnitude of the magnetic field, B with the distance, d from the centre of the conductor , is correctly represented by the figure: