Question 162: Magnetism and Matter

Question

There are two infinitely long straight current carrying conductors and they are held at right angles to each other so that their common ends meet at the origin as shown in the figure given below. The ratio of current in both conductor is 1 : 1. The magnetic field at point P is ____________.

Accepted Answer

B
due to wire (1)
= $${{{\mu _0}I} \over {4\pi y}}\left[ {\sin 90 + \sin {	heta _1}} ight]$$
$$ = {{{\mu _0}} \over {4\pi }}{I \over y}\left( {1 + {x \over {\sqrt {{x^2} + {y^2}} }}} ight)$$ ....(1)
B
due to wire (2)
= $${{{\mu _0}} \over {4\pi }}{1 \over x}(\sin 90^\circ  + \sin {	heta _2})$$
$$ = {{{\mu _0}} \over {4\pi }}{1 \over x}\left( {1 + {y \over {\sqrt {{x^2} + {y^2}} }}} ight)$$ ....(2)
Total magnetic field
$$B = {B_1} + {B_2}$$
$$B = {{{\mu _0}I} \over {4\pi }}\left[ {{1 \over y} + {x \over {y\sqrt {{x^2} + {y^2}} }} + {1 \over x} + {y \over {x\sqrt {{x^2} + {y^2}} }}} ight]$$
$$B = {{{\mu _0}I} \over {4\pi }}\left[ {{{x + y} \over {xy}} + {{{x^2} + {y^2}} \over {xy\sqrt {{x^2} + {y^2}} }}} ight]$$
$$B = {{{\mu _0}I} \over {4\pi }}\left[ {{{x + y} \over {xy}} + {{\sqrt {{x^2} + {y^2}} } \over {xy}}} ight]$$
$$B = {{{\mu _0}I} \over {4\pi xy}}\left[ {\sqrt {{x^2} + {y^2}}  + (x + y)} ight]$$
Option (1)

Answer

$${{{\mu _0}I} \over {4\pi xy}}\left[ {\sqrt {{x^2} + {y^2}}  + (x + y)} \right]$$

Answer

$${{{\mu _0}I} \over {4\pi xy}}\left[ {\sqrt {{x^2} + {y^2}}  - (x + y)} \right]$$

Answer

$${{{\mu _0}Ixy} \over {4\pi }}\left[ {\sqrt {{x^2} + {y^2}}  - (x + y)} \right]$$

Answer

$${{{\mu _0}Ixy} \over {4\pi }}\left[ {\sqrt {{x^2} + {y^2}}  + (x + y)} \right]$$

Magnetism and Matter

There are two infinitely long straight current carrying conductors and they are held at right angles to each other so that their common ends meet at the origin as shown in the figure given below. The ratio of current in both conductor is 1 : 1. The magnetic field at point P is ____________.

Choose the correct answer: