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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4.Four independent waves are expressed as \[ (i)\; y_1=A_1\sin\omega t, \] \[ (ii)\; y_2=A_2\sin 2\omega t, \] \[ (iii)\; y_3=A_3\cos\omega t, \] \[ (iv)\; y_4=A_4\sin\left(\omega t+\frac{\pi}{3}\right) \] The interference between two of these waves is possible in

5.Assertion (A) : The mass of a nucleus is less than the sum of the masses of the constituent nucleons. Reason (R) : Energy is absorbed when the nucleons are bound together to form a nucleus.

6. If Bohr’s quantization postulate (angular momentum \( = \frac{nh}{2\pi} \)) is a basic law of nature, it should be equally valid for the case of planetary motion also. Why, then, do we never speak of quantization of orbits of planets around the Sun? Explain.

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SUBSCRIBE TO OUR NEWS LETTER

2.
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