A toroidal solenoid is given which has inner and outer radii as 28cm and 29cm respectively. If it is constructed with 3700 turns of wire around the core and a current of 10A flows in it, then calculate the magnetic field inside the core of the toroid.

Question

A toroidal solenoid is given which has inner and outer radii as 28cm and 29cm respectively. If it is constructed with 3700 turns of wire around the core and a current of 10A flows in it, then calculate the magnetic field inside the core of the toroid. (A) 2.60× 10- 2 T (B) 2.60× 10- 3 T (C) 4.52× 10- 2 T (D) 4.52× 10- 3 T

Tardigrade Admin · Accepted Answer

the number of turns per unit length for the given toroid

n = \frac{N}{2 π r _{a v}}

The average radius of toroid

r_{a v} = 28.8 c m = 28.5 \times 1 0^{- 2} m

∴ n = \frac{3700}{2 \times 3.14 \times 28.5 \times 1 0 ^{- 2}} = 2067.27 \approx 2067

Now,

B = μ_{o} n I = 4 π \times 1 0^{- 7} \times 2067 \times 10

= 259615.2 \times 1 0^{- 7} T = 2.60 \times 1 0^{- 2} T

Q. A toroidal solenoid is given which has inner and outer radii as $28 c m$ and $29 c m$ respectively. If it is constructed with $3700$ turns of wire around the core and a current of $10 A$ flows in it, then calculate the magnetic field inside the core of the toroid.

$2.60 \times 1 0^{- 2} T$

$2.60 \times 1 0^{- 3} T$

$4.52 \times 1 0^{- 2} T$

$4.52 \times 1 0^{- 3} T$

Q. A toroidal solenoid is given which has inner and outer radii as 28cm and 29cm respectively. If it is constructed with 3700 turns of wire around the core and a current of 10A flows in it, then calculate the magnetic field inside the core of the toroid.

2.60×10−2T

2.60×10−3T

4.52×10−2T

4.52×10−3T

the number of turns per unit length for the given toroid n=2πrav​N​ The average radius of toroid rav​=28.8cm=28.5×10−2m ∴n=2×3.14×28.5×10−23700​=2067.27≈2067 Now, B=μo​nI=4π×10−7×2067×10 =259615.2×10−7T=2.60×10−2T

Q. A toroidal solenoid is given which has inner and outer radii as $28 c m$ and $29 c m$ respectively. If it is constructed with $3700$ turns of wire around the core and a current of $10 A$ flows in it, then calculate the magnetic field inside the core of the toroid.

$2.60 \times 1 0^{- 2} T$

$2.60 \times 1 0^{- 3} T$

$4.52 \times 1 0^{- 2} T$

$4.52 \times 1 0^{- 3} T$