Home
Class 12
PHYSICS
In Fig. infinite conducting rings each h...

In Fig. infinite conducting rings each having current i in the direciton shown are placed concentrically in the same plane as shown in the figure. The radii of rings are `r,2r,2^2r,2^3r,......,(oo)`. The magnetic field at the centre of rings will be

A

Zero

B

`(mu_(0)i)/(r)`

C

`(mu_(0)i)/(2r)`

D

`(mu_(0)i)/(3r)`

Text Solution

Verified by Experts

The correct Answer is:
D
`B=(mu_(0)i)/(2r)-(mu_(0)i)/(2(2r))+(mu_(0)i)/(2(2^(2)r))...(oo)`
`B=(mu_(0)i)/(2r) [1-1/2+1/(2^(2))-(1)/(2^3)+oo]`
`B=(mu_(0)i)/(2r)[(1)/(1-(-(1)/(2)))] implies B=(mu_(0)i)/(3r)`.
Promotional Banner

Topper's Solved these Questions

  • MISCELLANEOUS VOLUME 5

    CENGAGE PHYSICS ENGLISH|Exercise Multiple Correct|34 Videos

  • MISCELLANEOUS VOLUME 5

    CENGAGE PHYSICS ENGLISH|Exercise Linked Comprehension|84 Videos

  • MISCELLANEOUS VOLUME 3

    CENGAGE PHYSICS ENGLISH|Exercise True and False|3 Videos

  • NUCLEAR PHYSICS

    CENGAGE PHYSICS ENGLISH|Exercise ddp.5.5|14 Videos

Similar Questions

Explore conceptually related problems

A ring of the radius R is placed in the y - z plane and it carries a current i. The conducting wires which are used to supply the current to the ring can be assumed to be vary long and are placed as shown in the figure. The magnitude of the magnetic field at the centre of the ring A is

A conducting ring of radius r having charge q is rotating with angular velocity omega about its axes. Find the magnetic field at the centre of the ring.

A conducting ring of radius r having charge q is rotating with angular velocity omega about its axes. Find the magnetic field at the centre of the ring.

In the figure shown there are two semicircles of radii r_(1) and r_(2) in which a current i is flowing. The magnetic induction at the centre O will be

In the figure shown there are two semicircles of radii r_(1) and r_(2) in which a current i is flowing. The magnetic induction at the centre O will be

Can you use Ampere's law of find the magnetic field at the centre of a ring of radius R and carrying current l?

A conducting light string is wound on the rim of a metal ring of radius r and mass m . The free end of the string is fixed to the ceiling. A vertical infinite smooth conducting plane is always tangent to the ring as shown in the figure. A uniform magnetic field Bis applied perpendicular to the plane of the ring. The ring is always inside the magnetic field. The plane and the strip are connected by a resistance R . When the ring is released, find a. the curent in the resistance R as as function of time. b. the terminal velocity of the ring.

Find the direction of magnetic field at a point P due to two infinite current carrying wires shown in the figure. Given r_(1) gt r_(2)

A non-conducting ring of radius R having uniformly distributed charge Q starts rotating about x-x' axis passing through diameter with an angular acceleration alpha , as shown in the figure. Another small conducting ring having radius a(altltR) is kept fixed at the centre of bigger ring is such a way that axis xx' is passing through its centre and perpendicular to its plane. If the resistance of small ring is r = 1Omega , find the induced current in it in ampere. (Given q=(16xx10^(2))/(mu_(0))C, R=1m,a=0.1m,alpha="8rad s"^(-2)

A current I is flowing thorugh the loop. The direction of the current and the shpae of the loop are as the shown in the figure. The magnetic fild at the centre of the loop is (mu_(0) I)/(R) times (MA = R, MB = 2R, /_DMA = 90^(@))