A coil 3.85 cm radius, containing 450 turns, is placed in a uniform magnetic field that varies with time according to B=( 1.20×10−2 T/s )t+( 2.60×10−5 T/s4 )t4. The coil is connected to a 700-Ω resistor, and its plane is perpendicular to the magnetic field. You can ignore the resistance of the coil.

Find the magnitude of the induced emf in the coil as a function of time.

0.025V + (0.000218V/s³) t³

Explanation:

Parameters given:

Radius of coil, r = 3.85 cm = 0.0385 m

Number of turns, N = 450

Magnetic field, B = ( 1.20×10^(−2) T/s )t + (2.60×10^(−5) T/s4 )t^4.

The magnitude of Induced EMF is given as:

E = N * A * dB/dt

Where A is the area of the coil

First, we differentiate the magnetic field with respect to time:

dB/dt = 0.012 + 0.000104t³

Therefore, EMF will be:

E = 450 * 3.142 * (0.012 + 0.000104t³)

E = 2.096(0.012 + 0.000104t³)

E = 0.025V + (0.000218V/s³)t³

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