A) We need to calculate the Magnetic flux of a Solenoid,

Where B is the magnetic field and A the Area.

Here \mu_0 is the permeability constant, I the current and N number of turns.
Replacing we have,



B) We calculate the mutual inductance, so



c) We calculate the emf



Answer:
d = 120 [m]
Explanation:
In order to solve this problem, we must use the theorem of work and energy conservation. Where the energy in the final state (when the skater stops) is equal to the sum of the mechanical energy in the initial state plus the work done on the skater in the initial state.
The mechanical energy is equal to the sum of the potential energy plus the kinetic energy. As the track is horizontal there is no unevenness, in this way, there is no potential energy.
E₁ + W₁₋₂ = E₂
where:
E₁ = mechanical energy in the initial state [J] (units of Joules)
W₁₋₂ = work done between the states 1 and 2 [J]
E₂ = mechanical energy in the final state = 0
E₁ = Ek = kinetic energy [J]
E₁ = 0.5*m*v²
where:
m = mass = 60 [kg]
v = initial velocity = 12 [m/s]
Now, the work done is given by the product of the friction force by the distance. In this case, the work is negative because the friction force is acting in opposite direction to the movement of the skater.
W₁₋₂ = -f*d
where:
f = friction force = 36 [N]
d = distance [m]
Now we have:
0.5*m*v² - (f*d) = 0
0.5*60*(12)² - (36*d) = 0
4320 = 36*d
d = 120 [m]
Answer:
The constant force is 263.55 newtons
Explanation:
There's a rotational version of the Newton's second law that relates the net torque on an object with its angular acceleration by the equation:
(1)
with τ the net torque and α the angular acceleration. It’s interesting to note the similarity of that equation with the well-known equation F=ma. I that is the moment of inertia is like m in the linear case. The magnitude of a torque is defined as

with F the force applied in some point, r the distance of the point respect the axis rotation and θ the angle between the force and the radial vector that points toward the point the force is applied, in our case θ=90 and sinθ=1, then (1):
(2)
Because the applied force is constant the angular acceleration is constant too, and for constant angular acceleration we have that it's equal to the change of angular velocity over a period of time:

It's important to work in radian units so knowing that 
(3)
The moment of inertia of a disk is:
(4)
with M the mass of the disk and R its radius, then

using the values (3) and (4) on (2)
(2)
Because the force is applied about the rim of the disk r=R=1.50:

Answer:
when there is a change in the direction
Explanation:
The particle will move faster when there is a change in the direction on the movement
1. 9.04 s
We can find the time taken for the steel ball to reach the ground by using the SUVAT equation:

where
d = 400 m is the distance
u = 0 is the initial velocity of the ball
g = 9.8 m/s^2 is the acceleration of gravity
t is the time
Solving the formula for t, we find the time taken for the ball to reach the ground:

2. 88.6 m/s
The final velocity of the ball before it reaches the ground can be found by using the equation
v = u + gt
where
u is the initial velocity
g is the acceleration of gravity
t is the time
Here we have
u = 0
g = 9.8 m/s^2
Substituting the time of flight, t = 9.04 s, we find the final velocity:
