3. A metal square consists of four straight wires of length s and resistance R.

Question

3. A metal square consists of four straight wires of length s and resistance R. The square sits inside a unorm external magnetic teld pointing into the page. Iniialy, the field has strength B Buit starting at time t-Q,the field changes at a steady rate Speoficaly at the T-the teld ips sot at ends up pontrg out of tho KKRpage with strength B Between t-0andt T, what cunment ows around the square b. At t·T/2, the external magnesc held is momentaty zero. What cument fows around the square at that moment? c.Between t·Oand t . T2 the external Seld points into the KR Rpage, and decreases from B, to O. During this time interval does the current in the square ow clocowise or d, Between t TZ and t . The esterna held ports out of page and ncreases from to B During this time interval does the cument in the square fow dockwise or counterclockwise? e. At time t T/2, what is the magnetic field at the center of the square? (if you end up with a nasty integral don t try to integrate it

Explanation / Answer

a)

Here , induced current = induced EMF/R

induced current = rate of change of flux/R

induced current = s^2 * (2B/T) /R

   induced current = 2Bs^2/(T*R)

b) now, at t = T/2

as the field is changing at a constant rate ,

induced current is same ,

induced current = 2Bs^2/(T*R)

c)

Here , as the field is decreasing , the induced current will produced a

magnetic field supporting the applied field.

hence , the current is CLOCKWISE

d)

this time as the magnitude od field is increasing , the induced field will oppose this change and the direction of induced current is CLOCKWISE

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