An emf is induced in a conducting loop of wire 1.07 m long as its shape is changed from square to circular. find the average magnitude of the induced emf if the change in shape occurs in 4.36 s and the local 0.115-t magnetic field is perpendicular to the plane of the loop.

0.517 mV

Explanation:

Length of wire = 1.07 m

For square:

Perimeter = 1.07 m

Let a be the side of square

So, 4a = 1.07

a = 0.2675 m

Area of square, A 1 = side x side = 0.2675 x 0.2675 = 0.07156 m^2

For circle:

Circumference = 1.07 m

Let r be the radius of circle

So, 2 π r = 1.07

2 x 3.14 x r = 1.07

r = 0.1704 m

Area of circle, A 2 = π r^2 = 3.14 x 0.1704 x 0.1704 = 0.09115 m^2

Change in area, dA = A2 - A1 =   0.09115 - 0.07156  = 0.0196 m^2

Time taken in changing the area, dt = 4.36 s

Magnetic field, B = 0.115 T

According to the Farady's law of electromagnetic induction

e = 5.17 x 10^-4 V

e = 0.517 mV

Thus, the induced emf is 0.517 mV.

answer: at 24 february, 2014 the population gets twice of its initial population.

explanation:

since we have given that

the population for alpha city, t years after january 1, 2004 is given as

first we find out the initial population, i.e. t=0,

so, our quadratic equation becomes,

according to question, we have said that if the population has twice its initial population, then it becomes

so, time taken to reach this above mentioned population is given by

now, we know that time can't be negative so, we take t=9.149 years.

hence, at 24 february, 2014 the population gets twice of its initial population.