Magnetic Field Due to a Circular Arc at the Centre
A cell is con...
Question
A cell is connected between the points A and C of a circular conductor ABCD of centre O with angle =60∘. If B1 and B2 are the magnitudes of the magnetic fields at O due to the currents in ABC and ADC respectively, the ratio B1B2 is
A
0.2
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B
6
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C
1
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D
5
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Solution
The correct option is C1 Magnetic field due to part ABC, B1=μ0I12r×300360 B1=5×μ0I16×2r
Magnetic field due to part ADC, B2=μ0I22r×60360 B2=1×μ0I26×2r
B2B2=5i1i2
Now, both the circular elements can be imagined to be in a circuit as shown in the diagram. Since voltage is same across both the conductors. ∴i1i2=R2R1=l2l1 and l2l1=θ2θ1 ∴i1i2=θ2θ1=60300=15 B1B2=5×15=1