Charge to Mass Ratio with Speed Control

Caution: The number given by the coordinate tool is the diameter of the orbit, not the radius!

• $|F_{centripetal}| = m |v|^2/r$
• $\vec F_B = q \vec v \times \vec B \Rightarrow |F_B|= |q| |v| |B|$
• $|F_{centripetal}| = |F_B| \Rightarrow \frac{|q|}{m} = \frac{|v|}{|B|r}$

Charge to Mass Ratio with Electric Potential Control

Caution: The number given by the coordinate tool is the diameter of the orbit, not the radius!

• $|F_{centripetal}| = m |v|^2/r$
• $\vec F_B = q \vec v \times \vec B \Rightarrow |F_B|= |q| |v| |B|$
• $|F_{centripetal}| = |F_B| \Rightarrow \frac{|q|}{m} = \frac{|v|}{|B|r}$
• $|qV| = \frac{1}{2} m |v|^2 \Rightarrow |v| = \sqrt{2|V|\frac{|q|}{m}}$
• $\frac{|q|}{m} = \frac{\sqrt{2|V|\frac{|q|}{m}}}{|B|r} \Rightarrow \frac{|q|}{m} = \frac{2|V|}{|B|^2 r^2}$

Crossed Fields

Adjust the fields and the velocity to send the charge to the right horizontally (undeflected).
$\vec F_E = q \vec E$, $\vec F_B = q \vec v \times \vec B$
When the charge is undeflected:
$\vec F_E + \vec F_B = \vec 0 \Rightarrow |\vec E| = |\vec v \times \vec B|$.

Magnetic Field on Earth

Notice the geographical north actually carries south magnetic charge and vice versa.

Magnetic Field of a Coil

Magnetic Field of a Solenoid

Make Your Own Magnetic Field

Magnetic Force on an Electric Charge

Use the slider above to adjust the angle of the magnetic field.

Magnetic Force on Current

Use the slider above to adjust the angle of the magnetic field.

Magnetic Field of a Current

Magnetic Field of a Pair of Currents

Magnetic Flux

Magnetic flux is the amount of magenetic field captured by a surface. Adjust the sliders to see how the total flux changes.

Hall Effect

• The simulation shows a currrent flowing toward you. It can be represented by positive charge carriers with velocity pointing toward you, or negative charge carriers with velocity pointing away from you.
• Because $\vec F_B = q \vec v \times \vec B = (-q) (-\vec v) \times \vec B$, magnetic force does not change if you flip the signs of both $q$ and $\vec v$.
• Click on "Toggle Charge Carriers" to see that the charge carriers are pushed to the left no matter the sign of the charge.
• If the charge carriers are positive, their concentration on the left will generate a high electric potential on the left side.
• If the charge carriers are negative, their concentration on the left will generate a low electric potential on the left side.
• The potential difference, called the Hall voltage can be measured by a voltmeter connected across both sides of the conductor.

Electromagnetic Waves