Ampere's Law (Calculus) Video Lessons

Concept

# Problem: A metal ring 4.00 cm in diameter is placed between the north and south poles of large magnets with the plane its area perpendicular to the magnetic field. These magnets produce an initial uniform field of 1.12 T between them but are gradually pulled apart, causing this field to remain uniform but decrease steadily at 0.210 T/s.Part A. What is the magnitude of the electric field induced in the ring?Part B. In which direction (clockwise or counterclockwise) does the current flow as viewed by someone on the south pole of the magnet?

###### FREE Expert Solution

This problem uses Ampere's law, which is written as:

$\overline{){\mathbf{\int }}{\mathbf{E}}{\mathbf{·}}{\mathbf{d}}{\mathbf{l}}{\mathbf{=}}{\mathbf{A}}{\mathbf{·}}\frac{\mathbf{d}\mathbf{B}}{\mathbf{d}\mathbf{t}}}$

Part A.

From the Ampere's law,

dl = 2πR

A = πR2

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###### Problem Details

A metal ring 4.00 cm in diameter is placed between the north and south poles of large magnets with the plane its area perpendicular to the magnetic field. These magnets produce an initial uniform field of 1.12 T between them but are gradually pulled apart, causing this field to remain uniform but decrease steadily at 0.210 T/s.
Part A. What is the magnitude of the electric field induced in the ring?
Part B. In which direction (clockwise or counterclockwise) does the current flow as viewed by someone on the south pole of the magnet?