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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A light copper ring is freely suspended by a light string. A bar magnet is held horizontally with its length along the axis of the ring. The magnet is moved towards the ring with its N pole facing the loop. What will happen to the ring and its position? Explain.

2.
Two small identical metallic balls having charges \( q \) and \( -2q \) are kept far at a separation \( r \). They are brought in contact and then separated at distance \( \frac{r}{2} \). Compared to the initial force \( F \), they will now:

3.
Draw the number of scattered particles versus the scattering angle graph for scattering of alpha particles by a thin foil. Write two important conclusions that can be drawn from this plot.

5.
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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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CBSE CLASS XII Related Questions

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2.Two small identical metallic balls having charges \( q \) and \( -2q \) are kept far at a separation \( r \). They are brought in contact and then separated at distance \( \frac{r}{2} \). Compared to the initial force \( F \), they will now:

3. Draw the number of scattered particles versus the scattering angle graph for scattering of alpha particles by a thin foil. Write two important conclusions that can be drawn from this plot.

5.Photoemission of electrons occurs from a metal (\( \phi_0 = 1.96 \, \text{eV} \)) when light of frequency \( 6.4 \times 10^{14} \, \text{Hz} \) is incident on it. Calculate: Energy of a photon in the incident light, The maximum kinetic energy of the emitted electrons, and The stopping potential.

6.A square loop of side 0.50 m is placed in a uniform magnetic field of 0.4 T perpendicular to the plane of the loop. The loop is rotated through an angle of 60° in 0.2 s. The value of emf induced in the loop will be:

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Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
A light copper ring is freely suspended by a light string. A bar magnet is held horizontally with its length along the axis of the ring. The magnet is moved towards the ring with its N pole facing the loop. What will happen to the ring and its position? Explain.

2.
Two small identical metallic balls having charges \( q \) and \( -2q \) are kept far at a separation \( r \). They are brought in contact and then separated at distance \( \frac{r}{2} \). Compared to the initial force \( F \), they will now:

3.
Draw the number of scattered particles versus the scattering angle graph for scattering of alpha particles by a thin foil. Write two important conclusions that can be drawn from this plot.

5.
Photoemission of electrons occurs from a metal (\( \phi_0 = 1.96 \, \text{eV} \)) when light of frequency \( 6.4 \times 10^{14} \, \text{Hz} \) is incident on it. Calculate: Energy of a photon in the incident light, The maximum kinetic energy of the emitted electrons, and The stopping potential.

6.
A square loop of side 0.50 m is placed in a uniform magnetic field of 0.4 T perpendicular to the plane of the loop. The loop is rotated through an angle of 60° in 0.2 s. The value of emf induced in the loop will be: