Question

In the 2009 film 2012, there is a scene in which a supervolcano erupts under Yellowstone National Park. It has been fairly recently discovered that in at least some volcanic eruptions, the magnetic field of the earth is reversed in the region of the volcano (only while it is erupting). The magnetic field during this eruption would have a magnitude of 5.3 ⋅ 10−4 ? and be oriented 68.6∘ south of down. During the eruption, there is a pyroclastic flow (this is the fast lava-looking “liquid” that flows down the volcano first), which can move at speeds upwards of 200 ?⁄?. One particular rock flowing in this has a mass of 150 ????? and an electric charge of +1.2 ⋅ 104 ?.

1. Find the Lorentz (magnetic) force (magnitude and direction) acting on this rock when it has just started flowing near the top of the volcano. At this point, it flows at a speed of 50 ?⁄? vertically downward.

2. Find the Lorentz (magnetic) force (magnitude and direction) acting on this rock when it has just reached the bottom of the volcano. At this point, it flows at a speed of 200 ?⁄? horizontally east.

Answer 1

Sol: Here angle between horizontal and magnetic field is and B = 5.3x10^-4T

speed v1 =50 m/s v2 = 200 m/s mass m = 150g =0.15kg charge q = +1.2x10^4 C

Now here horizontal component of magnetic field is

and the vertical component is

Now the Lorentz (magnetic) force (magnitude and direction) acting on this rock when it has just started flowing near the top of the volcano. At this point, it flows at a speed of v1=50 ?⁄? vertically downward.

And it will be directed toward West.

And the Lorentz (magnetic) force (magnitude and direction) acting on this rock when it has just reached the bottom of the volcano. At this point, it flows at a speed of v2= 200 ?⁄? horizontally east is given as-

It will be directed toward North.