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  4. A cell is connected between the points A and C of a circular conductor ABCD with 0 as centre and angle textAOC text= 6 text0 texto text. If textB text1 and textB2 are the magnitudes of the magnetic fields at O due to the currents in ABC and ADC respectively, then ratio (B1/B2) is :

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Q. 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 :Physics Question Image

WBJEEWBJEE 2006

Solution:

$\begin{array}{l} B =\frac{\mu_0}{4 \pi} \frac{\theta i }{ r } \Rightarrow B \propto \theta i \quad\left(\text { but } \frac{ i _1}{ i _2}=\frac{ l _2}{ l _1}=\frac{\theta_2}{\theta_1}\right) \\ \Rightarrow \frac{ B _1}{ B _2}=\frac{\theta_1}{\theta_2} \cdot \frac{ i _1}{ i _2} \\ \text { So, } \frac{ B _1}{ B _2}=\frac{\theta_1}{\theta_2} \times \frac{\theta_2}{\theta_1} \\ \Rightarrow B _1= B _2 \\ \frac{ B _1}{ B _2}=1 \end{array}$