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WB JEE Medical WB JEE Medical Solved Paper-2006

  • question_answer
    A cell is connected between the points A and C of a circular conductor ABCD with 0 as centre and angle \[\text{AOC}\,\text{= 6}{{\text{0}}^{\text{o}}}\text{.}\]If \[{{\text{B}}_{\text{1}}}\]and \[{{\text{B}}_{2}}\]are the magnitudes of the magnetic fields at O due to the currents in ABC and ADC respectively, then ratio \[\frac{{{B}_{1}}}{{{B}_{2}}}\]is :

    A)  1                                            

    B)  2

    C)  5                                            

    D)  6

    Correct Answer: C

    Solution :

                     From Biot-savart law the magnetic field at the centre is directly proportional to the length of current carrying segment. \[\therefore \]           \[\frac{{{B}_{1}}}{{{B}_{2}}}=\frac{\text{length}\,\text{of}\,\text{ABC}}{\text{length}\,\text{of}\,\text{ADC}}\] \[\text{=}\frac{\text{angle}\,\text{subtended}\,\text{by}\,\text{ABC}}{\text{angle}\,\text{subtended}\,\text{by}\,\text{AD}\text{C}}\] \[=\frac{({{360}^{o}}-{{60}^{o}})}{{{60}^{o}}}=\frac{300}{60}=\frac{5}{1}\]


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