Answer:
Q = 6.33μC
Explanation:
To find the value of the charge Q you take into account both gravitational force and electric force over each ball. By symmetry you can use the fact that both balls experiences the same forces. Hence you only take into account the forces for one ball for the x component and y component:
M: mass of the ball = 0.09kg
T: tension of the string
F_e: electric force between charges
angle = 45°
The electric force is given by:
Q: charge of the balls
r: distance between balls = 2m
You divide both equation in order to eliminate the tension T:
By doing Q the subject of the formula and replacing you obtain:
hence, the charge of the balls is 6.33μC
Answer:
a) fem = - 2.1514 10⁻⁴ V, b) I = - 64.0 10⁻³ A, c) P = 1.38 10⁻⁶ W
Explanation:
This exercise is about Faraday's law
fem = 
where the magnetic flux is
Ф = B x A
the bold are vectors
A = π r²
we assume that the angle between the magnetic field and the normal to the area is zero
fem = - B π 2r dr/dt = - 2π B r v
linear and angular velocity are related
v = w r
w = 2π f
v = 2π f r
we substitute
fem = - 2π B r (2π f r)
fem = -4π² B f r²
For the magnetic field of Jupiter we use the equatorial field B = 428 10⁻⁶T
we reduce the magnitudes to the SI system
f = 2 rev / s (2π rad / 1 rev) = 4π Hz
we calculate
fem = - 4π² 428 10⁻⁶ 4π 0.10²
fem = - 16π³ 428 10⁻⁶ 0.010
fem = - 2.1514 10⁻⁴ V
for the current let's use Ohm's law
V = I R
I = V / R
I = -2.1514 10⁻⁴ / 0.00336
I = - 64.0 10⁻³ A
Electric power is
P = V I
P = 2.1514 10⁻⁴ 64.0 10⁻³
P = 1.38 10⁻⁶ W
One of the useful forns of the formula for electrical power is: Power = (voltage squared) / (resistance). Knowing that power is proportional to (voltage squared), we can see that if the voltage is reduced to 1/2, the power is reduced to 1/4 of its original value. The 220volt/60watt appliance, when operated on 110 volts, dissipates 60/4 = 15 watts.
