Answer:
F = 2π I R B
Explanation:
The magnetic force is described by the equation.
F = q v x B = i L x B
Where i is the current, L is a vector that points in the direction of the current (length) and B is the magnetic field.
This equation can be used in scalar form and the direction of the force found by the right hand ruler, the thumb goes in the direction of L, the fingers extended in the direction of B and the palm of the hand indicates the direction of the force if the load is positive
F = i L B sin θ
In this case the wire is in the xy plane and the z-axis field whereby they are perpendicular, θ = 90º and sin 90 = 1
F = i L B
The loop length is
L = 2π R
F = i 2π R B
F = 2π I R B
The force is in the loop
Three times larger I think.
The equation of motion of a pendulum is:
where 
it its length and 
is the gravitational acceleration. Notice that the mass is absent from the equation! This is quite hard to solve, but for <em>small</em> angles (
), we can use:
Additionally, let us define:
We can now write:
The solution to this differential equation is:
where 
and 
are constants to be determined using the initial conditions. Notice that they will not have any influence on the period, since it is given simply by:
This justifies that the period depends only on the pendulum's length.
