Relationships Between Force, Field, Energy, Potential Video Lessons

Concept

# Problem: Consider an experimental setup where charged particles (electrons or protons) are first accelerated by an electric field and then injected into a region of constant magnetic field with a field strength of 0.25 T. What is potential difference, in volts, required in the first part of the experiment to accelerate electrons to a speed of 6.1x107 m/s?

###### FREE Expert Solution

Kinetic energy:

$\overline{){\mathbf{K}}{\mathbf{=}}\frac{\mathbf{1}}{\mathbf{2}}{{\mathbf{mv}}}^{{\mathbf{2}}}}$

Potential energy:

$\overline{){\mathbf{∆}}{\mathbf{U}}{\mathbf{=}}{\mathbf{q}}{\mathbf{·}}{\mathbf{∆}}{\mathbf{V}}}$

Law of conservation of energy:

$\overline{){{\mathbf{K}}}_{{\mathbf{i}}}{\mathbf{+}}{{\mathbf{U}}}_{{\mathbf{i}}}{\mathbf{+}}{{\mathbf{W}}}_{{\mathbf{nc}}}{\mathbf{=}}{{\mathbf{K}}}_{{\mathbf{f}}}{\mathbf{+}}{{\mathbf{U}}}_{{\mathbf{f}}}}$

Wnc is the work done by non-conservative forces.

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###### Problem Details

Consider an experimental setup where charged particles (electrons or protons) are first accelerated by an electric field and then injected into a region of constant magnetic field with a field strength of 0.25 T.

What is potential difference, in volts, required in the first part of the experiment to accelerate electrons to a speed of 6.1x107 m/s?