As shown in the figure, a metallic wire of resistance 0.20 slides on a horizontal, U-shaped metallic rail. The separation between the parallel arms is 20 cm . When the wire is slid at a rate of 20 cm s ⁻¹ , an electric current of 2.0 A passes through it. Determine the dip at the place, given that the horizontal component of the earth's magnetic field is 3.0 10⁻⁵ T .

Step-by-step solution

The motional EMF induced in the sliding wire is due to the vertical component of the Earth's magnetic field, as the wire moves in a horizontal plane. The induced EMF is given by: = B_V l v where B_V is the vertical component of the magnetic field, l is the length of the wire, and v is its velocity. According to Ohm's law, the induced current is: I = R = B_V l v R Rearranging for B_V : B_V = I R l v Given values are: I = 2.0 10⁻⁶ A R = 0.20 l = 20 cm = 0.2 m v = 20 cm s ⁻¹ = 0.2 m s ⁻¹ Substituting these values: B_V