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denis-greek [22]
3 years ago
5

A solid conducting sphere with radius R carries a positive total charge Q. The sphere is surrounded by an insulating shell with

inner radius R and outer radius 2R. The insulating shell has a uniform charge density rho.
Part A

Find the value of rho so that the net charge of the entire system is zero.

Express your answer in terms of the variables Q, R, and appropriate constants.Part B

If rho has the value found in part A, find the magnitude of the electric field in the region 0
Express your answer in terms of the variables Q, R, r, and appropriate constants.Part C

If rho has the value found in part A, find the magnitude of the electric field in the region R
Express your answer in terms of the variables Q, R, r, and appropriate constants.Part D

If rho has the value found in part A, find the direction of the electric field in the region R
If rho has the value found in part A, find the magnitude of the electric field in the region r>2R.

Express your answer in terms of the variables Q, R, r, and appropriate constants.Part F

As a general rule, the electric field is discontinuous only at locations where there is a thin sheet of charge. Explain how your results in previous parts agree with this rule.
Physics
1 answer:
Illusion [34]3 years ago
8 0

Answer:

Explanation:

Volume of the insulating shell is,

V_{shell}=\frac{4}{3}\pi(R^3_2-R^3_1)

Charge density of the shell is,

\rho=\frac{Q_{shell}}{\frac{4}{3}\pi(R^3_2-R^3_1)}

Here, R_2 =2R, R_1 =R \,and\, Q_{shell} =-Q

\rho=\frac{Q_{shell}}{\frac{4}{3}\pi((2R)^3-R^3)}=\frac{-3Q}{28\piR^3}

B)

The electric field is E=\frac{1}{4\pi\epsilon_0}\frac{Qr}{R^3}

For 0 <r<R the electric field is zero, because the electric field inside the conductor is zero.

C)

For R <r <2R According to gauss law

E(4\pi r^2)=\frac{Q}{\epsilon_0}+\frac{4\pi\rho}{3\epsilon_0}(r^3-R^3)

substitute \rho=\frac{-3Q}{28\piR^3}

E=\frac{2}{7\pi\epsilon_0}\frac{Q}{r^2}-\frac{Qr}{28\piR^3}

D)

The net charge enclosed for each r in this range is positive and the electric field is outward

E)

For r>2R

Charge enclosed is zero, so electric field is zero

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First, we have to establish the <u>reference system</u>. Let's assume that the building is on the negative y-axis and that the brick was thrown at the origin (see figure attached).

According to this, the initial velocity V_{o} has two components, because the brick was thrown at an angle \alpha=61\º:

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V_{ox}=8.6\frac{m}{s}cos(61\º)=4.169\frac{m}{s}  (2)

V_{oy}=V_{o}sin\alpha   (3)

V_{oy}=8.6\frac{m}{s}sin(61\º)=7.521\frac{m}{s}   (4)

As this is a projectile motion, we have two principal equations related:

<h2>In the x-axis: </h2>

X=V_{ox}.t  (5)

Where:

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If we already know X and V_{ox}, we have to find the time (we will need it for the following equation):

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t=2.42s  (7)

<h2>In the y-axis: </h2>

-y=V_{oy}.t+\frac{1}{2}g.t^{2}   (8)

Where:

y is the height of the building (<u>in this case it has a negative sign because of the reference system we chose)</u>

g=-9.8\frac{m}{s^{2}} is the acceleration due gravity

Substituting the known values, including the time we found on equation (7) in equation (8), we will find the height of the building:

-y=(7.521\frac{m}{s})(2.42s)+\frac{1}{2}(-9.8\frac{m}{s^{2}}).(2.42s)^{2}   (9)

-y=-10.52m   (10)

Multiplying by -1 each side of the equation:

y=10.52m >>>>This is the height of the building

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