Answer:
Number of turns per unit length will be 
Explanation:
We have given that strength of the magnetic field produced by the solenoid B = 7 T
Current in the solenoid i = 200 A
Let the number of turns per unit length is n
Magnetic field due to solenoid is given as
here
is permeability of free space n is number of turns per unit length and i is current
So 

We are given that,

We need to find
when 
The equation that relates x and
can be written as,


Differentiating each side with respect to t, we get,



Replacing the value of the velocity


The value of
could be found if we know the length of the beam. With this value the equation can be approximated to the relationship between the sides of the triangle that is being formed in order to obtain the numerical value. If this relation is known for the value of x = 6ft, the mathematical relation is obtained. I will add a numerical example (although the answer would end in the previous point) If the length of the beam was 10, then we would have to



Search light is rotating at a rate of 0.96rad/s
Answer:
P = 4.5 watts
Explanation:
Given that,
EMF of the circuit, E = 3 volt
The resistance of the resistors, R = 2 ohms
We need to find the power of this circuit. The relation between power, emf and resistance is given by the formula as follows :

Substitute all the values,

So, the power of this circuit is equal to 4.5 watts.
Answer: The box was moving with a velocity of 0.256m/s when it hit the spring
Explanation: Please see the attachments below