Two concentric conducting spherical shells produce a radially outward electric field of magnitude 49,000 n/c at a point 4.10 m from the center of the shells. the outer surface of the larger shell has a radius of 3.75 m. if the inner shell contains an excess charge of -5.30 μc, find the amount of charge on the outer surface of the larger shell. (k = 1/(4πε0) = 8.99 × 109 n · m2/c2)

the electric charge in the outher layer is = 97.12 μC

Explanation:

The equation for electric field E caused by an electric charge is:

E= K*Q/d^(2)     (1)

Where K = 8.99*10^(9)   Nm^(2)/C^(2)        K = 1/4*π*ε₀  

Q is the electric charge and d is distance between the electric charge and the point where the field is requiered

In this case by simetry the electric field produced for 2 concentric shells  could be calculated as the electric charge where at the center of the concentric shell.

the shells produce and outward field and  the inner shell have a charge of -5,30 μC; this mean that the outside shell must have a positive ( an greater charge) in order to get an outward field

So:

E = 49000 N/C

d = 4.10 m then   d^(2)  is  (4.10)^(2) = 16.81 m^(2)

q electric charge in the inner shell    -5.5 μC o -5,5* 10^(-6)

Then using a gaussian surface (an sphere with the same center as the shells we are able to apply equation (1) and get the net charge of the shells

E = K* Q(n) / r^(2)                     Q (n)  = E* r^(2) /K

Q (n) = (49000* 16.81   Nm^(2)/C )/8.99*10^(9)   Nm^(2)/C^(2)

Q(n) = 91622* 10^(-9)C or 91,62 10^(-6)C or 91.62 μC

Then the charge in the outside shell is 91,62 + 5,5 μC  = 97.12 μC

the force required to move the cart is divided by three or 33.33 n.

russian is not my first language, so i'm afraid i can't write out an answer in russian, but hopefully you can find a way to do so. here's my best translation of the problem: you're given a plot of a particle's position in one-dimensional space over time, and you're asked to find either the total distance traveled by the particle after 6 seconds had elapsed, or the total displacement of the particle after 6 seconds.

if you want the total distance traveled, you would first need to determine the particle's velocity as a function of time, then integrate that over the 6-second interval. we know the position function is quadratic with roots at 0 and 6, so we have

where is unknown. because the position is parabolic, there is symmetry about the midpoint at , and we know that

so that the position function is

which means the velocity is

then the total distance traveled is

so the total distance traveled is 20 m.

on the other hand, if you want to find displacement: the particle starts at and ends at , so its displacement is 0.