The wire loop PQRSP formed by joining tw...

The wire loop `PQRSP` formed by joining two semicircular wires of radii ` R_(1)` and `R_(2)` carries a current `I` as shown . The magnitude of the magnetic induction at the center `C` is ………..

Text Solution

Verified by Experts

The effect of current in PQ and RS for producing mangnetic field
at centre is zero.
Magnetic field due to current in semi-
circular arc `QAR=1/2[(mu_0)/2 I/(R_1)]` dir-
ected towards the reader perpendicu-
lar to the plane of paper.
Magnetic field due to current in semicircular arc `SBP=1/2[(mu_0)/2 I/(R_2)]`
directed away form the reader perpendicular to the plane of paper.
`:. Net magnetic field =1/2[(mu_0)/2 I/(R_1)]-1/2[(mu_0)/2 I/(R_2)]`
(directed towards the reader perpendicular to plane of paper).
`=(mu_0)/4[ I/(R_1)- I/(R_2)]`

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The wire loop PQRS formed by joining two semi circular wires of radii R_(1) , and _(2) Ry carries a current I as shown the figure. The inagnitude of magnetic induction at the centre O is

`(mu_(0)I)/(4)((1)/(R_(2))-(1)/(R_(1)))`

`(mu_(0)I)/(4)((1)/(R_(1))-(1)/(R_(2)))`

`mu_(0)I((1)/(R_(2))-(1)/(R_(1)))`

`mu_(0)I((1)/(R_(1))-(1)/(R_(2)))`

The wire loop ABCDEA formed by joining two semicircular loops of radii R_1 and R_2 carries a current I. What is the magnetic induction at the center O in the following figure?

`(mu_0i)/4(1/(R^(1))-1/(R^(2)))`

`(mu_0i)/4(R^(2)-R^(2))`

`(mu_0i)/4(R^(2)+R^(2))`

`(mu_0i)/4(1/(R^(2))-1/(R^(2)))`

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

`(mu_(0)i)/r(r_(1)+r_(2))`

`(mu_(0)i)/4(r_(1)-r_(2))`

`(mu_(0)i)/4((r_(1)+r_(2))/(r_(1)r_(2)))`

`(mu_(0)i)/4((r_(1)-r_(2))/(r_(1)r_(2)))`