Which of the following statements are true?
check all that apply.
a) a time-varying electric field will produce a magnetic field.
b) electric and magnetic fields can be treated independently only if they vary in time.
c) time-varying electric and magnetic fields can propagate through space only if there is no matter in their path.
d) a time-varying magnetic field will produce an electric field.

A) A time-varying electric field will produce a magnetic field.

D) A time-varying magnetic field will produce an electric field.

Explanation:

As we know that time varying electric field can induce displacement current in the space

So we will have

now we have

so it will induce magnetic field given as

Now similarly time varying magnetic field can induce electric field by Faraday's law given as

now we have

so we have

so induce electric field is due to magnetic field

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.