A circular coil has 500 turns and a radius 14 cm. The coil is moved in 0.35 seconds from an area...

Question:

A circular coil has 500 turns and a radius 14 cm. The coil is moved in 0.35 seconds from an area where there is no magnetic field into an area with a magnetic field of strength {eq}6.7 \times 10^{-2}\ T {/eq}. The coil remains perpendicular to the magnetic field at all times.

a) Find the magnitude of the induced EMF in the coil.

b) If the coil has a resistance of 2.7 Ω, find the current in the coil.

c) After moving into the field, the coil now remains stationary in the field for 3 seconds. Find the current induced in the coil during this interval.

Faraday's Law

Faraday's Law states that the magnitude of the emf induced in a loop is directly proportional to the rate of change of the magnetic flux linked with the loop, mathematically

{eq}\begin{align} \epsilon = \frac{N\Delta \Phi}{\Delta t} \end{align} {/eq}

Where {eq}\Delta \Phi {/eq} is the change in the magnetic flux, N is the number of turns in the loop, and {eq}\Delta t {/eq} is the time taken.

Answer and Explanation:

Data Given

  • Number of turns in the coil {eq}N = 500 {/eq}
  • Radius of the coil {eq}r = 14 \ \rm cm = 0.14 \ \rm m {/eq}
  • The final magnetic field linked with the coil {eq}B_f = 6.7 \times 10^{-2} \ \rm T {/eq}
  • Time elapsed {eq}\Delta t = 0.35 \ \rm s {/eq}
  • Resistance of the coil {eq}R = 2.7 \ \Omega {/eq}

Part A) Let us use the Faraday's law to calculate the emf induced in the loop

{eq}\begin{align} \epsilon = \frac{N\Delta \Phi}{\Delta t} \end{align} {/eq}

{eq}\begin{align} \epsilon = \frac{NA \Delta B)}{\Delta t} \end{align} {/eq}

{eq}\begin{align} \epsilon = \frac{500 \times \pi \times (0.14\ \rm m)^2 \times (6.7 \times 10^{-2} \ \rm T-0 \ \rm T)}{0.35 \ \rm s} \end{align} {/eq}

{eq}\begin{align} \color{blue}{\boxed{ \ \epsilon = 5.89 \ \rm V \ }} \end{align} {/eq}


Part B) Currnt in the coil, using Ohm's law

{eq}\begin{align} I = \frac{V}{R} \\ I = \frac{ 5.89 \ \rm V}{2.7 \ \rm \Omega} \\ \color{blue}{\boxed{ \ I = 2.2 \ \rm A \ }} \end{align} {/eq}


Part C) As the coil is stationary in the field for the 3 s it means the flux linked with coil remains constant and induced emf and hence induced current during this interval will be zero.

{eq}\begin{align} \color{blue}{\boxed{ \ I' =0 \ \rm A \ }} \end{align} {/eq}


Learn more about this topic:

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Faraday's Law of Electromagnetic Induction: Equation and Application

from High School Physics: Help and Review

Chapter 13 / Lesson 10
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