Question

A rectangle measuring 30.0 cm by 40.0 cm is located inside a region of a spatially uniform magnetic field of 1.65 T, with the field perpendicular to the plane of the coil (Figure 1). The coil is pulled out at a steady rate of 2.00 cm/s traveling perpendicular to the field lines. The region of the field ends abruptly as shown.
a) Find the emf induced in this coil when it is all inside the field.
b) Find the emf induced in this coil when it is partly inside the field.
c) Find the emf induced in this coil when it is all outside the field.

Answer 1

The solution for the questions below is mathematically given as

• induced emf=0
• induced emf=0.0132V
• induced emf=0

What is the emf induced in this coil when it is all inside the field.?

(A)

Generally, the equation for the flux is  mathematically given as

$\Phi _{B}=B.A$

$\Phi _{B}=B.A\\\\\Phi _{B}=B(40*30*10^{-4}) ,$

So, the magnetic flux through the coil is constant.

From faradays law,

$\varepsilon =-\frac{\mathrm{d} \Phi _{B}}{\mathrm{d} t}$

---(1) for the induced emf. Since magnetic flux is constant, LHS. of (1) =0

induced emf=0

(B)

Let x be the length of the coil's magnetic field area.

$then, \Phi _{B}=B.A=B(40*x*10^{-4}) \\\\\frac{\mathrm{d}\Phi _{B} }{\mathrm{d} t}=40\\B*10^{-4}*\frac{\mathrm{d} x}{\mathrm{d} t}$

induced emf=0.0132V

(C)

In conclusion, Therefore, there is no variation in the magnetic flux across the coil when magnetic flux=0.

induced emf=0

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