Given: B = 5 * 10-5 T ẑ; σ = 4 (Ohm-meters)-1 (conductivity) a) Assume that seawater is moving at a constant velocity v = v0 ŷ and that the Earth’s magnetic field is along the ẑ-direction. Calculate the electric current density J produced by the magnetic force. Hint: first compute the force per unit charge, F/q, and then use the relationship J = σ(F/q). b) Derive the equation of motion of a cylindrical differential volume element of base area δA and height δh parallel to the direction of J. Assume that seawater has a known volumetric mass density ρ. Show that this equation implies that the velocity satisfies the following differential equation: dvy/dt = vy/τ where τ is a constant that you should write in terms of B, σ, and ρ.
Given: B = 5 * 10-5 T ẑ; σ = 4 (Ohm-meters)-1 (conductivity)
a) Assume that seawater is moving at a constant velocity v = v0 ŷ and that the Earth’s magnetic field is along the ẑ-direction. Calculate the
b) Derive the equation of motion of a cylindrical differential volume element of base area δA and height δh parallel
to the direction of J. Assume that seawater has a known volumetric mass density ρ. Show that this equation implies that the velocity satisfies the following differential equation:
dvy/dt = vy/τ
where τ is a constant that you should write in terms of B, σ, and ρ.
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