Question

A 0.45-m metal rod moves 0.11 m in a direction that is perpendicular to a 0.80-T magnetic field in an elapsed time of 0.036 s. Assuming that the acceleration of the rod is zero m/s2, determine the emf that exists between the ends of the rod.

Answer 1

Answer:

(B) This cannot be determined without knowing the orientation of the rod relative to the magnetic field.

Because, Since acceleration of the rod is Zero. So, net force acting on the rod will be zero. But, its not specified that whether the rod is moving along varying magnetic field direction or a constant magnetic field direction.

Answer 2

The emf that exists between the ends of the rod is 3.53 V.

Area of the metal rod

Assuming the diameter of the rod = 0.45 m

$A = \frac{\pi d^2}{4} = \frac{\pi (0.45)^2}{4} \\\\A = 0.159 \ m^2$

Emf that exists between ends of the rod

$emf = -\frac{d\Phi}{dt}$

Ф = BAcosθ

$emf = - \frac{BAcos\theta_f - B A cos\theta _i}{t} \\\\emf = -BA(\frac{cos\theta_f - cos\theta _i}{t} )\\\\emf = -(0.8 \times 0.159)(\frac{cos90 - cos0}{0.036} )\\\\emf = 3.53 \ V$

Thus, the emf that exists between the ends of the rod is 3.53 V.

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