Home
Class 12
PHYSICS
Magnetic field in the cylindrical regaio...

Magnetic field in the cylindrical regaion with its axis passing through O varies at a constant rate `(dB)/(dt)`. A treangular imaginary loop ABC, with `AB = BC`, is lying in this region as shown in the adjacent figure. The work done to move unit positive charge from A to B along the side AB is

A

`r^(2)(dB)/(dt)`

B

`pir^(2)(dB)/(dt)`

C

`(r^(2))/(2)(dB)/(dt)`

D

`(3r^(2))/(4)(dB)/(dt)`

Text Solution

Verified by Experts

The correct Answer is:
C
No e.m.f. will be induced in AC because electric lines of force are perpendicular to AC and e.m.f. induced in `AB=` e.m.f. induced in BC.
`:.` e.m.f. induced in `AB=(1)/(2)|(dphi)/(dt)|=(1)/(2)r^(2)(dB)/(dt)`
Promotional Banner

Similar Questions

Explore conceptually related problems

Magnetic field B in a cylindrical region of radius r varies according to the law B = B_(0)t as shown in the figure. A fixed conducting loop ABCDA of resistance R is lying in the region as show . The current flowing through the loop is

The magnetic field in the cylindrical region shown in figure increase at a constant rate of 20mT//sec . Each side of the square loop ABCD has a length of 1 cm and resistance of 4Omega . Find the current in the wire AB if the switch S is closed

A charge q is uniformly distributed along the periphery of a non conducting uniform circular disc pivoted at its centre in a vertical plane and can freely rotate about a horizontal axis passing through its centre. A cylindrical region with its axis passing through the centre of the disc has a varying magnetic field B = kt as shown in the adjacent figure. wrapped over the disc as shown and remains stationary, then

A uniform magnetic field is restricted within a region of radius r. The magnetic field changes with time at a rate (dB)/(dt) . Loop 1 of radius R gt r encloses the region r and loop 2 of radius R is outside the region of magnetic field as shown in figure. Then, the emf generated is Zero in loop 1 and zero in loop 2 − d B d t π r 2 in loop 1 and − d B d t π 2 in loop 2 − d B d t π R 2 in loop 1 and zero in loop 2 − d B d t π r 2 in loop 1 and zero in loop 2

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 uniform but time varying magnetic field exists in a cylindrical region as shown in the figure. The direction of magnetic field is into the plane of the paper and its magnitude is decreasing at a constant rate of 2xx10^-3T//s . A particle of charge 1muC is moved slowly along circle of radius 1m by an external force as shown in figure. The plane of the circle of radius 1m by an external force as shown in figure. The plane of he circle lies in the plane of the paper and it is concentric with the cylindrical region. The work done by the external force in moving this charge along the circle will be

In the figure B_(1) , B_(2) and B_(3) represent uniform time varying magnetic fields in three different infinitely long cylindrical regions with axis passing through P , Q and R and perpendicular to the plane of the paper. PQR is an equilateral triangle of side 4sqrt(3)r , where r is radius of each cylindrical region (r=1m) . The magnetic inductions vary with time t as B_(1)=A+at , B_(2)=A-bt and B_(3)=A+ct . Here a=2 Tesla//s , b=2 Tesla//s and c=1 Tesla//s and A is a constant with dimensions of magnetic field and 't' is time. Find the induced electric field strength at the centroid of the triangle PQR .

A uniform magnetic field along a long cylindrical rod varies with time as (B = alpha t) , where alpha is positive constant. The electric field inside the rod as a function of radial distance r from the central axis is proportional to

The are AB with the centre C and infinitely long wire having linear charge density lambda are lying in the same plane. The minium amount of work to be done to move a point charge q_(0) from point A to B through a circular path AB of radius a is equal to

The arc AB with the centre C and the infinitely long wire having linear charge density lambda are lying in the same place. The minimum amount of work to be done to move a point charge q_(0) from point A to B through a circuit path AB of radius a is equal to