(Solved): As shown above, a circular loop of radius r is made with a conducting wire of resistance R. There is ...
As shown above, a circular loop of radius r is made with a conducting wire of resistance R. There is a uniform magnetic field B! all over space that is perpendicular to the plane of the loop and directed out of the paper. Calculate the induced emf in the loop, the current in the loop, and determine the direction of the current (explain briefly), when:
a) The magnitude of the magnetic field B = B is constant:
b) B changes in time as B(t)=a+bt, where a,b>0
c) B changes in time as B(t)= a - bt .
Now let’s again assume that B is constant, as in part (a). Then in each of the following situations, is there an induced current in the loop? Explain briefly without calculations:
(i) When the loop moves around staying on the plane.
(ii) When the loop rotates around a perpendicular axis through its center.
(iii) When the loop rotates around an axis on the plane of the loop and going through its center.
Expert Answer
The circular loop has radius and resistance .The magnetic field in the region is and is out of the page.Magnetic flux through the loop is (Where area of loop is , its direction is out of the page)Induced emf in the loop is Induced current in the loop is By Lenz's law, induced current is in such a direction which opposes the initial changing magnetic field which produced it.-----------a) Magnetic field is constant.Magnetic flux through the loop is Hence , Induced emf Induced current Hence no direction for current.b) Magnetic flux Induced emf Induced current Magnetic field is increasing with time. Outward magnetic flux is increasing. Hence induced current is in clockwise direction.