Question

Figure (35-E4) shows a long wire bent at the middle to form a right angle.Show that the magnitudes of the magnetic fields at the points P,Q,R and S are equal and find this magnitude.

Answer 1

At point P, B due to $W_1=0$

B due to $W_2=\frac{{\mu }_{0}i}{2\pi d}along⨂$

So, $netB=\frac{{\mu }_{0}i}{2\pi d}along⨂$

At point Q,

B due to $W_1=\frac{{\mu }_{0}i}{2\pi d}along⨂$

B due to $W_2=0$

So, $netB=\frac{{\mu }_{0}i}{2\pi d}along$

At point R, B due to $W_1=0$

B due to $W_2=\frac{{\mu }_{0}i}{2\pi d}along$

Hence $netB=\frac{{\mu }_{0}i}{2\pi d}along$

At point S, B due to $W=\frac{{\mu }_{0}i}{2\pi d}along⨂$

B due to $W_2=0$

So, $netB=\frac{{\mu }_{0}i}{2\pi d}along⨂$

Clearly magnitude of B at each P,Q,R and S is $\frac{{\mu }_{0}i}{2\pi d}$.