A long solenoid has 200 turns per cm and carries a current i. The magnetic field at its centre is 6.28 × 10−2weber/m2. Another long solenoid has 100 turns per cm and it carries a current i/3. The value of the magnetic field at its centre is

B=μ0ni B∝ni B1B2=n1n2×i1i2 6.28×10−2B2=200100i(i/3) 6.28×10−2B2=6⇒B2=6.28×10−26 =1.05×10−2wb/m2

A long solenoid has 200 turns per cm and carries a current i. The magnetic field at its centre is 6.28 × 10−2weber/m2. Another long solenoid has 100 turns per cm and it carries a current i/3. The value of the magnetic field at its centre is

B=μ0ni B∝ni B1B2=n1n2×i1i2 6.28×10−2B2=200100i(i/3) 6.28×10−2B2=6⇒B2=6.28×10−26 =1.05×10−2wb/m2

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A long solenoid has 200 turns per cm and carries a current i. The magnetic field at its centre is $6.28 \times 10^{- 2} w e b e r / m^{2}$ . Another long solenoid has 100 turns per cm and it carries a current i/3. The value of the magnetic field at its centre is

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$1.05 \times 10^{- 4} w b / m^{2}$

$1.05 \times 10^{- 2} w b / m^{2}$

$1.05 \times 10^{- 5} w b / m^{2}$

$1.05 \times 10^{- 3} w b / m^{2}$

answer is B.

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Detailed Solution

$B = μ_{0} n i$

$B \propto n i$

$\frac{B_{1}}{B_{2}} = \frac{n_{1}}{n_{2}} \times \frac{i_{1}}{i_{2}}$

$\frac{6.28 \times 10^{- 2}}{B_{2}} = \frac{200}{100} \frac{i}{(i / 3)}$

$\frac{6.28 \times 10^{- 2}}{B_{2}} = 6 \Rightarrow B_{2} = \frac{6.28 \times 10^{- 2}}{6}$

= $1.05 \times 10^{- 2} w b / m^{2}$

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