Acircular loop of flexible iron wire has an initial circumference of 165cm , but its circumference is decreasing at a constant rate of 12.0 cm/s due to a tangential pull on the wire. the loop is in a constant, uniform magnetic field oriented perpendicular to the plane of the loop of magnitude 0.500 t part a find the emf induced in the loop, at the instant when 9.0s have passed. and find the direction

emf induced is 0.005445 V and direction is clockwise because we can see area is decrease and so that flux also decrease so using right hand rule direction of current here clockwise

Explanation:

Given data

initial circumference = 165 cm

rate = 12.0 cm/s

magnitude = 0.500 T

tome = 9 sec

to find out

emf induced and direction

solution

we know emf in loop is - d∅/dt    ........1

here ∅ = ( BAcosθ)

so we say angle is zero degree and magnetic filed is uniform here so that

emf = - d ( BAcos0) /dt

emf = - B dA /dt     ..............2

so  area will be

dA/dt = d(πr²) / dt

dA/dt = 2πr dr/dt

we know 2πr = c,

r = c/2π = 165 / 2π

r  = 26.27 cm

c is circumference so from equation 2

emf = - B 2πr dr/dt    ................3

and

here we find rate of change of radius that is

dr/dt = 12/2π = 1.91  cm/s

so when 9.0s have passed that radius of coil = 26.27 - 191 (9)

radius = 9.08 cm

so now from equation 3 we find emf

emf = - (0.500 )  2π(9.08 )   1.91  

emf = - 0.005445

and magnitude of emf = 0.005445 V

so

emf induced is 0.005445 V and direction is clockwise because we can see area is decrease and so that flux also decrease so using right hand rule direction of current here clockwise