M2.2.Circle Wire
Problem: Suppose that on the circle
,
,
there is a constant current along
direction.
a) Calculate the corresponding magnetic field at a point
b) if the circle is located on the
c) If a moving point charge
,
,
is located at the point
and
.
, Calculate the magnetic field.
with the velocity
, Calculate the
with the velocity
, Calculate the
magnetic force acting on the point charge .
d) If a moving point charge
is located at the point
magnetic force acting on the point charge .
Solution:
The volumetric current distribution for the current:
Position vector:
Length of the vector:
Differential volume in Cylindrical coordinates:
a) Substitute them into the volumetric integral
where
Try to solve problem with a similar manner at
On the center of the wire, magnetic field is
b)
c)
d)
.