Two concentric coplanar circular loops of wire (resistance per unit length 10 -4 ohms m-1) have diameters 0.2 m and 2 m. With time-varying potential difference of (4+2.5t) applied to larger loop, find current in smaller one.

Magnetic field at O (centre) due to larger loop’s current equals = B = μ₀I/2R

Now, assuming that r is resistance per unit length, then the following can be said:

I = potential difference/resistance = 4 + 2.5t/2πR⋅ρ $\times$ πr²

$\therefore$ Thus, it can also be expressed as:

⇒ B = μ₀/2R $\times$ 4 + 2.5t/2πR . ρ

⇒ r < ϕ = B × πr²= μ₀/2R $\times$ 4 + 2.5t/2πR . ρ $\times$ πr²

Thus, the Induced emf can be expressed as, e = dϕ/dt

= μ₀r²/4R²ρ $\times$ 2.5

Corresponding current in smaller loop is = I′

Therefore,

⇒ I′ = e/R = μ₀r²/4R²ρ × 2.5 × 1/2πrρ

= 2.5μ₀r/8πR²ρ²

= 2.5 $\times$ 4π $\times$ 10⁻⁷$\times$ 0.1/8π $\times$ (1)²$\times$ (10⁻⁴)²

$\therefore$ I′ = 1.25 A

Hence, the current in smaller loop is 1.25 A

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Two concentric coplanar circular loops of wire (resistance per unit length 10 -4 ohms m-1) have diameters 0.2 m and 2 m. With time-varying potential difference of (4+2.5t) applied to larger loop, find current in smaller one.

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Consider the nuclear reaction \( X \to Y + Z \). Let \( M_x \), \( M_y \), and \( M_z \) be the masses of the three nuclei X, Y, and Z respectively. Then which of the following relations hold true?

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Two concentric coplanar circular loops of wire (resistance per unit length 10 -4 ohms m-1) have diameters 0.2 m and 2 m. With time-varying potential difference of (4+2.5t) applied to larger loop, find current in smaller one.

Related Questions

CBSE CLASS XII Related Questions

1.A magnet held vertically, with its north pole down, is dropped along the axis of a closed solenoid placed vertically on a table. If the observer looks down from the top,

2.The number of free electrons per unit volume ($\text{m}^3$) in a wire made of copper (resistivity $1.72 \times 10^{-8}\,\Omega\,\text{m}$) is $8.5 \times 10^{28}$. Calculate the average number of collisions made by an electron in one second when an electric field is maintained in the wire.

4.Consider the nuclear reaction \( X \to Y + Z \). Let \( M_x \), \( M_y \), and \( M_z \) be the masses of the three nuclei X, Y, and Z respectively. Then which of the following relations hold true?

Similar Physics Concepts

Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
A magnet held vertically, with its north pole down, is dropped along the axis of a closed solenoid placed vertically on a table. If the observer looks down from the top,

2.
The number of free electrons per unit volume ($\text{m}^3$) in a wire made of copper (resistivity $1.72 \times 10^{-8}\,\Omega\,\text{m}$) is $8.5 \times 10^{28}$. Calculate the average number of collisions made by an electron in one second when an electric field is maintained in the wire.

4.
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