Answer:
Explanation:
The volume of a sphere is:
V = 4/3 * π * a^3
The volume charge density would then be:
p = Q/V
p = 3*Q/(4 * π * a^3)
If the charge density depends on the radius:
p = f(r) = k * r
I integrate the charge density in spherical coordinates. The charge density integrated in the whole volume is equal to total charge.





Since p = k*r
Q = p*π^2*r^3 / 2
Then:
p(r) = 2*Q / (π^2*r^3)
Answer:
Torque,
Explanation:
Given that,
The loop is positioned at an angle of 30 degrees.
Current in the loop, I = 0.5 A
The magnitude of the magnetic field is 0.300 T, B = 0.3 T
We need to find the net torque about the vertical axis of the current loop due to the interaction of the current with the magnetic field. We know that the torque is given by :

Let us assume that, 
is the angle between normal and the magnetic field, 
Torque is given by :

So, the net torque about the vertical axis is
. Hence, this is the required solution.
Answer:
The direction of the field is downward, and negatively charged particles will experience an upwards force due to the field.
F = N e E where E is the value of the field and N e the charge Q
M g = N e E and M g is the weight of the drop
N = M g / (e E)
N = 1.1E-4 * 9.8 / (1.6E-19 * 370) = 1.1 * 9.8 / (1.6 * 370) * E15 = 1.82E13
.00011 kg is a very large drop
Q = N e = M g / E = .00011 * 9.8 / 370 = 2.91E-6 Coulombs
Check: N = Q / e = 2.91E-6 / 1.6E-19 = 1.82E13 electrons
(a) As the car is moving with constant velocity, it means the rate change of velocity does not change, therefore the average acceleration of the car is zero.
Thus, there is no acceleration, when velocity is constant.
(b) Average acceleration,

Here, v is final velocity and u is the initial velocity and
is the time interval.
As twelve seconds later, the car is halfway around the track and traveling in the opposite direction with the same speed, therefore

Thus, the average acceleration of the car is
in the direction to the left.