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

the minimum constant speed at which she can catch the train is 2.7 m/s

given:

acceleration = 0.6

time = 4.5 s

to find:

velocity = ?

formula used:

from 1st kinematic equation we get,

v = u + at

u = initial speed of train = 0 m/s

v = final speed of the train

a = acceleration of the train

t = time

solution:

from 1st kinematic equation we get,

v = u + at

u = initial speed of train = 0 m/s

v = final speed of the train

a = acceleration of the train

t = time

v = 0 + (0.6 × 4.5)

v = 2.7 m/s

the minimum constant speed at which she can catch the train is 2.7 m/s

the components of a vector are the parts of the vectors that are to each other.

b perpendicular