Question
Two large metal sheets carry surface currents as shown in figure. The current through a strip of width dl is Kdl where K is a constant. Find the magnetic field at the points P, Q and R.
✓
Answer
At point P, i = 0, Thus B = 0
At point R, i = 0, B = 0
At point $\theta,$
Applying ampere’s rule to the above rectangle
$\text{B}\times2\text{l}=\mu_0\text{K}_0\int\limits_\text{o}^\text{l}\text{dl}$
$\text{B}\times2\text{l}=\mu_0\text{Kl}\Rightarrow\text{B}=\frac{\mu_0\text{K}}{2}$
$\text{B}\times2\text{l}=\mu_0\text{K}_0\int\limits_\text{o}^\text{l}\text{dl}$
$\text{B}\times2\text{l}=\mu_0\text{Kl}\Rightarrow\text{B}=\frac{\mu_0\text{K}}{2}$
Since the $\overrightarrow{\text{B}}$ due to the 2 stripes are along the same direction, thus.
$\text{B}_\text{net}=\frac{\mu_0\text{K}}{2}+\frac{\mu_0\text{K}}{2}=\mu_0\text{k}$
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