Aspherical cavity is hollowed out of the interior of aneutral conducting sphere. at the center of the cavity is a pointcharge, of positive charge q. a) what is the total surface charge q_int on the interior surface of the conductor (i. e., onthe wall of the cavity)? b) what is the magnitude e_int of the electric field inside the cavity as a function ofthe distance rfrom the point charge? let k, as usual, denote \frac{1}{4\pi\epsilon_0} .c) what is the electric field e_ext outside the conductor?

A) the total surface charge on the interior surface is equal in module to q+ and oposite in charge ().

B) The electric field inside the cavity is: .

C) The electric field outside the cavity is: .

Explanation:

The spherical cavity has a neutral charge. This means that this spherical cavity won´t affect the field inside. Therefore the field generated by the charge q+ is the same with or without the spherical cavity.

The total charge of the system can be calculated considering charge conservation:

Qtot0=Qtotf

q(+)=q(+)+qin+qex

qin=-qex and qin+qex=0

Using a Gaussian sphear centered in the charge q(+), we can calculate the field knowing that its direction would be .

If we apply the gaussian sphear between the interior and the exterior radius of the conducting hollow sphear, knowing that the field should be 0:

If we apply the gaussian sphear outside the exterior radius of the conducting hollow sphear, we obtain the field required in c).

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.