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A uniform current carrying ring of mass ...

A uniform current carrying ring of mass `m` and radius `R` is connected by a massless string as shown in Fig. 1.142. A uniform magnetic field `B_0` exists in the region to keep the ring in horizontal position, then the current in the ring is (l=length of string)
.

A

`(mg)/(piRB_0)`

B

`(mg)/(RB_0)`

C

`(mg)/(3piRB_0)`

D

`(mgl)/(piR^2B_0)`

Text Solution

Verified by Experts

The correct Answer is:
a
Torque due to magnetic field `tau_(mag)=MB_0=ipiR^2B_0....(i)`
Torque due to weight about the point where string is connected
`tau_("weight")=mgR....(ii)`
If ring remains horizontal, then `tau_(mag)=tau_("weight")`
`IpiR^2B_0=mgRimpliesI=(mg)/(piRB_0)`.
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