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A magnetic field B = 20.0 mT points in the +y-direction. A rectangular circuit of wire with an area of 200 cm2, which is initially in the xz-plane, rotates into the xy-plane as shown. If this process is smooth and takes 1.2 seconds, what is the magnitude of the emf induced in the loop?

A Magnetic Field B 200 MT Points In The Ydirection A Rectangular Circuit Of Wire With An Area Of 200 Cm2 Which Is Initially In The Xzplane Rotates Into The Xypl class=

Sagot :

nuhulawal20

If the process is smooth and only takes the given time, the magnitude of the emf induced in the loop is 3.33 × 10⁻⁴Volts.

Given the data in the question

  • Magnetic field; [tex]B = 20mT = 20 * 10^{-3}T[/tex]
  • Area; [tex]A = 200cm^2 = 0.02m^2[/tex]
  • Time; [tex]\delta t = 1.2s[/tex]

Magnitude of the emf induced in the loop; [tex]|e| =\ ?[/tex]

From Faraday's law, formula for Induced emf is given as:

[tex]|e| = -\frac{\delta\theta}{\delta t} \\\\|e| = -\frac{\delta (BAcos\theta)}{\delta t} \\\\|e| = -BA\frac{\delta (cos\theta)}{\delta t}[/tex]

Where [tex]\delta\theta[/tex] is the change in flux, [tex]\delta t[/tex] is time taken to change the flux, B is the Magnetic field and A is the area.

We know that; [tex]\theta = 0^o\ to\ 90^o[/tex], so

[tex]|e| = -BA\frac{(cos90^o -cos0^o)}{\delta t}[/tex]

Now, we substitute in our given valueslux

[tex]|e| = [-(20*10^{-3}T)*0.02m^2]\frac{(cos90^o -cos0^o)}{1.2s}\\\\|e| = (-0.0004Tm^2)\frac{(0-1)}{1.2s}\\\\|e| = \frac{0.0004Tm^2}{1.2s}\\\\|e| = 3.33*10^{-4}Volts[/tex]

Therefore, if the process is smooth and only takes the given time, the magnitude of the emf induced in the loop is 3.33 × 10⁻⁴Volts

Learn more: https://brainly.com/question/17110955

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