Question

Help with current and magnetic field problem

Answer 1

Two large, flat current-carrying sheets are placed parallel to each other, one sheet above the other. The upper sheet carries a current of 2.0 A per unit of width tot he left, and the lower sheet carries a current of 5.0 A per unit of width to the right. Calculate the magnitude of the magnetic field:

a). between the sheets
b). above the the upper sheet
c). below the bottom sheet


I know that Ampere's law is:\[\int\limits B*dl=\mu_0I_{enclosed}\]But I'm not really sure where to go..
Would a). be \(B=\mu_0 (\Delta I) L\) ?

Answer 2

where \(\Delta I\) is the difference between the two currents

Answer 3

@IrishBoy123 @Michele_Laino

Answer 4

what do u think the answer is

Answer 5

@madib12 I already posted my work and attempt at the solution.

Answer 6

magnetic field produced by a plane of current is like below:

Answer 7

where \(I_s\) is the current of surface, namely \(I_s=2.0 \;Amperes\), \(B_r,B_l\) are the magnetic fields, due to the current, at the left and at the right of the plane respectively.
Now using the subsequent equation of Maxwell:
\[\large {\text{rot }}{\mathbf{B}} = \frac{{4\pi }}{c}{\mathbf{J}}\]
and symmetry of our physical system, we can write this:
\[\large {{\mathbf{B}}_r} = \frac{{2\pi }}{c}{I_s}{\mathbf{\hat z}},\quad {{\mathbf{B}}_l} = - \frac{{2\pi }}{c}{I_s}{\mathbf{\hat z}}\]
where \(\large {{\mathbf{\hat z}}}\) is the unit vector as below:

please note that, I'm using the \(CGS\) system