A) Zero mark
B) 10 cm mark
C) 3 cm mark
D) 6 cm mark.
Correct Answer: C
Solution :
Current carrying wires are shown in the figure. In region 1 and 3 magnetic fields produced by both the conductors have same direction so they will add on. In region 2, magnetic fields produced by both the conductors are not same, so there is possibility to get a point where net magnetic field is zero. Let P be the point where net magnetic field will be zero. Here, AP = r BP = (4 - r) \[{{l}_{1}}=1\,A,{{l}_{2}}=3A\] Magnetic field produced by a current carrying conductor at a distance r from it, \[B=\frac{{{\mu }_{o}}l}{2\pi r}\] For conductor, I \[{{B}_{1}}=\frac{{{\mu }_{o}}{{l}_{1}}}{2\pi r}\] For conductor, II \[{{B}_{{{l}_{2}}}}=\frac{{{\mu }_{o}}{{l}_{2}}}{2\pi (4-r)}\] Net magnetic field at P is zero so, \[{{B}_{1}}={{B}_{2}}\] \[\frac{{{\mu }_{0}}{{l}_{1}}}{2\pi r}=\frac{{{\mu }_{0}}{{l}_{2}}}{2\pi (4-r)}\] \[\Rightarrow \]\[(4-r){{l}_{1}}={{l}_{2}}\,r\] \[\Rightarrow \]\[1(4-r)=3r\] \[\Rightarrow \]\[4r=4\therefore \,r=1\,cm\] Position of the point P on the scale = 2+1 = 3 cm
You need to login to perform this action.
You will be redirected in
3 sec
