question_answer

20 A current is flowing in a long straight wire. The intensity of magnetic field at a distance of 10 m from the wire, will be

A)  \[\text{4}\times \text{l}{{\text{0}}^{-\text{5}}}\text{Wb}/{{\text{m}}^{\text{2}}}\]      

B)  \[\text{2}\times \text{l}{{\text{0}}^{-\text{5}}}\text{Wb}/{{\text{m}}^{\text{2}}}\]

C)  \[3\times {{10}^{-5}}\,Wb/{{m}^{2}}\] 

D)  \[\text{8}\times \text{l}{{\text{0}}^{-5}}\text{Wb}/{{\text{m}}^{\text{2}}}\]

Correct Answer: A

Solution :

                 Intensity of magnetic field produced due to straight current carrying wire will be                 \[B=\frac{{{\mu }_{0}}}{4\pi }\frac{2I}{r}\]                 Given,   \[I=20\,A\],                 r = 10 cm                 \[=10\times {{10}^{-2}}m\] \[\therefore \]  \[B={{10}^{-7}}\times \frac{2\times 20}{10\times {{10}^{-2}}}\]                 \[=4\times {{10}^{-5}}Wb/{{m}^{2}}\]