Sign in
12thPass logo
New chatPYQ LibraryDoubtsRank report
Sign in to see Recents

Your guest activity stays on this device

Sign in to save progress →
Sign in

Electromagnetic Induction question

2020 · 3 Sep · Shift 1 · Q54
Guest · filters and generic practice availableBrowsing as a guest · PYQ filters and generic practice are available. Sign in only for personalised features and saved progress.
  1. PYQ Library
  2. /JEE Main
  3. /Physics
  4. /Electromagnetic Induction
  5. /2020 · 3 Sep · Shift 1 · Q54

Electromagnetic Induction question

2020 · 3 Sep · Shift 1 · Q54

JEE MainPhysicsElectromagnetic InductionMCQ+4 / −1
An elliptical loop having resistance R, of semi major axis a, and semi minor axis b is placed in magnetic field as shown in the figure. If the loop is rotated about the x-axis with angular frequency ω\omegaω, the average power loss in the loop due to Joule heating is : JEE Main 2020 (Online) 3rd September Morning Slot Physics - Electromagnetic Induction Question 85 English
  1. A
    πabBωR{{\pi abB\omega } \over R}RπabBω​
  2. B
    π2a2b2B2ω2R{{{\pi ^2}{a^2}{b^2}{B^2}{\omega ^2}} \over R}Rπ2a2b2B2ω2​
  3. C
    π2a2b2B2ω22R{{{\pi ^2}{a^2}{b^2}{B^2}{\omega ^2}} \over {2R}}2Rπ2a2b2B2ω2​
  4. D
    Zero
View written solutionFree

Correct answer: C

  1. Magnetic flux through the rotating loop

The area of the elliptical loop is A=πab.A=\pi ab.A=πab.

If the loop rotates about the xxx-axis with angular speed ω\omegaω, then the angle between the magnetic field B⃗\vec BB and the area vector of the loop changes as θ=ωt.\theta = \omega t.θ=ωt.

Hence the magnetic flux through the loop is Φ=BAcos⁡θ=B(πab)cos⁡(ωt).\Phi = BA\cos\theta = B(\pi ab)\cos(\omega t).Φ=BAcosθ=B(πab)cos(ωt).

So, Φ=πabBcos⁡(ωt).\Phi = \pi abB\cos(\omega t).Φ=πabBcos(ωt).

  1. Induced emf

By Faraday's law, e=−dΦdt.e = -\frac{d\Phi}{dt}.e=−dtdΦ​.

Therefore,

= \pi abB\omega \sin(\omega t).$$ Thus the instantaneous emf magnitude is $$e(t)=\pi abB\omega \sin(\omega t).$$ 3. **Instantaneous current** Since the loop has resistance $R$, $$i(t)=\frac{e(t)}{R}=\frac{\pi abB\omega}{R}\sin(\omega t).$$ 4. **Instantaneous Joule heating power** Power dissipated is $$P(t)=i^2R=\frac{e^2}{R}.$$ So, $$P(t)=\frac{(\pi abB\omega)^2}{R}\sin^2(\omega t).$$ 5. **Average power over one cycle** The average value of $\sin^2(\omega t)$ over a complete cycle is $$\langle \sin^2(\omega t)\rangle = \frac12.$$ Hence, $$P_{\text{avg}}=\frac{(\pi abB\omega)^2}{R}\cdot \frac12 =\frac{\pi^2 a^2 b^2 B^2 \omega^2}{2R}.$$ 6. **Option check** - **A:** $\dfrac{\pi abB\omega}{R}$ — incorrect (dimensionally power does not match) - **B:** $\dfrac{\pi^2 a^2 b^2 B^2 \omega^2}{R}$ — misses factor $\frac12$ - **C:** $\dfrac{\pi^2 a^2 b^2 B^2 \omega^2}{2R}$ — correct - **D:** Zero — incorrect Therefore, the correct answer is **C**.
PreviousNext

More from Electromagnetic Induction

  • A uniform magnetic field B exists in a direction perpendicular to the plane of a square loop made of a metal wire. The wire has a diameter of 4 mm and a total length of 30 cm. The magnetic field changes with time at a steady rate dtdB​…2020 · MCQ
  • A small bar magnet is moved through a coil at constant speed from one end to the other. Which of the following series of observations will be seen on the galvanometer G attached across the coil? Three positions shown describe : (a) the… Includes diagram2020 · MCQ
  • Two concentric circular coils, C1 and C2 are placed in the XY plane. C1 has 500 turns, and a radius of 1 cm. C2 has 200 turns and radius of 20 cm. C2 carries a time dependent current I(t) = (5t2 – 2t + 3) A where t is in s. The emf induced…2020 · Numerical
  • An infinitely long, straight wire carrying current I, one side opened rectangular loop and a conductor C with a sliding connector are located in the same plane, as shown, in the figure. The connector has length l and resistance R. It… Includes diagram2020 · MCQ
  • A part of a complete circuit is shown in the figure. At some instant, the value of current I is 1A and it is decreasing at a rate of 102 A s–1. The value of the potential difference VP – VQ , (in volts) at that instant, is ​… Includes diagram2020 · Numerical
  • A long solenoid of radius R carries a time (t) - dependent current I(t)=I0t(1 - t). A ring of radius 2R is placed coaxially near its middle. During the time interval 0 ≤ t ≤ 1, the induced current (IR) and the induced EMF(VR) in…2020 · MCQ
  • Consider a circular coil of wire carrying constant current I, forming a magnetic dipole. The magnetic flux through an infinite plane that contains the circular coil and excluding the circular coil area is given by ϕ i. The magnetic…2020 · MCQ
  • A loop ABCDEFA of straight edges has six corner points A(0, 0, 0), B(5, 0, 0), C(5, 5, 0), D (0, 5, 0), E(0, 5, 5) and F(0, 0, 5). The magnetic field in this region is B=(3i+4k)T .…2020 · Numerical