A 1.0 meter long rod is held horizontally in the east-west direction on a distant planet and is dropped from a height of 1.23 m. The horizontal component of the planet's magnetic field is 6.93e-05 T. Find the emf induced between the ends of the rod just before it hits the ground.

Respuesta :

Answer:

The induced emf between two end is [tex]34.02 \times 10^{-5}[/tex] V

Explanation:

Given:

Length of rod [tex]l = 1[/tex] m

Height [tex]h = 1.23[/tex] m

Magnetic field [tex]B = 6.93 \times 10^{-5}[/tex] T

For finding induced emf,

  [tex]\epsilon = Blv[/tex]

Where [tex]v =[/tex] velocity of rod,

For finding the velocity of rod.

From kinematics equation,

 [tex]v^{2} = v_{o} ^{2} + 2gh[/tex]

Where [tex]v_{o} =[/tex] initial velocity, [tex]g = 9.8 \frac{m}{s^{2} }[/tex]

   [tex]v = \sqrt{2gh}[/tex]

   [tex]v = \sqrt{2 \times 9.8 \times 1.23}[/tex]

   [tex]v = 4.91[/tex] [tex]\frac{m}{s}[/tex]

Put the velocity in above equation,

   [tex]\epsilon = 6.93 \times 10^{-5} \times 1 \times 4.91[/tex]

   [tex]\epsilon = 34.02 \times 10^{-5}[/tex] V

Therefore, the induced emf between two end is [tex]34.02 \times 10^{-5}[/tex] V