A solid insulating sphere of radius R = 1.0 m that carries a positive charge Q1 = 1.0 mC uniformly distributed over it is concen
tric with a very thin insulating shell of radius 2R that carries the charge Q2 = -1.0 mC. The charge Q2 is distributed uniformly over the shell.
Use Gauss's law to obtain the magnitude of the electric field:
a. E1 inside the sphere, r < R
b. E2 between the sphere and the shell, R < r < 2R
c. E3 outside the shell, r > 2R
d. Plot the electric field in the radial direction on a graph. Be sure to label the actual magnitude of the electric field at r = 0, r= R, and r = 2R.
Use Gauss's law to obtain the magnitude of the electric field:
a. E1 inside the sphere, r < R
b. E2 between the sphere and the shell, R < r < 2R
c. E3 outside the shell, r > 2R
d. Plot the electric field in the radial direction on a graph. Be sure to label the actual magnitude of the electric field at r = 0, r= R, and r = 2R.
1 answer:
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Answer:
0.00903 rad
0.00926 rad
6.268\times 10^{-6}
Explanation:
s = Diameter of the object
r = Distance between the Earth and the object
Angle subtended is given by
For the Moon
The angle subtended by the Moon is 0.00903 rad
For the Sun
The angle subtended by the Sun is 0.00926 rad
Area ratio is given by
The area ratio is
a) 4 forces
b) 186 N
c) 246 N
Explanation:
a)
Let's count the forces acting on the bicylist:
1) Weight (): this is the gravitational force exerted on the bicyclist by the Earth, which pulls the bicyclist towards the Earth's centre; so, this force acts downward (m = mass of the bicyclist, g = acceleration due to gravity)
2) Normal reaction (N): this is the reaction force exerted by the road on the bicyclist. This force acts vertically upward, and it balances the weight, so its magnitude is equal to the weight of the bicyclist, and its direction is opposite
3) Applied force (): this is the force exerted by the bicylicist to push the bike forward. Its direction is forward
4) Air drag (): this is the force exerted by the air on the bicyclist and resisting the motion of the bike; its direction is opposite to the motion of the bike, so it is in the backward direction
So, we have 4 forces in total.
b)
Here we can find the net force on the bicyclist by using Newton's second law of motion, which states that the net force acting on a body is equal to the product between the mass of the body and its acceleration:
where
is the net force
m is the mass of the body
a is its acceleration
In this problem we have:
m = 60 kg is the mass of the bicyclist
is its acceleration
Substituting, we find the net force on the bicyclist:
c)
We can write the net force acting on the bicyclist in the horizontal direction as the resultant of the two forces acting along this direction, so:
where:
is the net force
is the applied force (forward)
is the air drag (backward)
In this problem we have:
is the net force (found in part b)
is the magnitude of the air drag
Solving for , we find the force produced by the bicyclist while pedaling: