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Question: The inner and outer radius of a toroid core are 28 cm and 29 cm respectively and around the core 370...

The inner and outer radius of a toroid core are 28 cm and 29 cm respectively and around the core 3700 turns of a wire are wounded. If the current in the wire is 10 A, then the magnetic field inside the core of the toroid is

A

2.60 × 10-2 T

B

2.60 × 10-2 T

C

4.52 × 10-2 T

D

4.52 × 10-2 T

Answer

2.60 × 10-2 T

Explanation

Solution

The number of turns per unit length for the given toroid

n=N2πrav\mathrm { n } = \frac { \mathrm { N } } { 2 \pi \mathrm { r } _ { \mathrm { av } } }

The average radius of toroid

rav=28+292=28.5 cm=28.5×10−2 m\mathrm { r } _ { \mathrm { av } } = \frac { 28 + 29 } { 2 } = 28.5 \mathrm {~cm} = 28.5 \times 10 ^ { - 2 } \mathrm {~m}

∴n=37002×3.14×28.5×10−2=2067.27≈2067\therefore \mathrm { n } = \frac { 3700 } { 2 \times 3.14 \times 28.5 \times 10 ^ { - 2 } } = 2067.27 \approx 2067

Now,

=259615.2×10−7 T=2.60×10−2 T= 259615.2 \times 10 ^ { - 7 } \mathrm {~T} = 2.60 \times 10 ^ { - 2 } \mathrm {~T}