41. Two circular coils 1 and 2 are made from
the same wire but the radius of the 1st coil
is twice that of the 2nd coil. What potential
difference in volts should be applied across
them so that the magnetic field at their
centres is the same?
(a) 2
(b) 3
(c) 4
(d) 6. (2006)
2. A very long straight wire carries a current I
Answers
Answer:
4 times of first coil
Explanation:
Magnetic feild due to first coil and second coil is same at center.
Then magnetic field B at center is,
B = μ₀I₁ / 2(2r) = μ₀I₂ / 2(r) = I₁/I₂ = 2 ....... (1)
As we know that Resistance of coil is related as,
R = ρ(L/A) where ρ=resistivity ,l=length ,A=area of cross section.
ρ and A is same for both coil but , I₁ = 2π(2r) and l₂ = 2π(r)
If V₁ and V₂ applied across first and second coil then,
I₁ = V₁ / R₁ and I₂ = V₂ / R₂
I₁ = V₁/[ ρ(L₁/A) ] .......... (2)
I₂ = V₂/[ρ(L₂/A)] ......... (3)
from equation 1, 2, 3
V₁/I₁ × I₂V₂ = 2
V₂/V₁ × I₂/I₁ = 2
V₁/V₂ × 1/2 = 2
V₁/V₂ = 4
V₁ = 4V₂
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