Magnetic Force and Right-Hand Rule: Physics Notes for Charges and Fields

Right-hand rule

Determines the direction of the magnetic force on a moving positive charge.

Magnetic force requirement

The charge must be moving with a component perpendicular to B.

Magnetic force direction on positive charge

Point fingers along velocity, curl toward B, thumb gives F.

Finding magnetic force direction for an electron

Use right-hand rule and reverse the result.

Velocity parallel to magnetic field

Force is zero.

Force direction for a proton moving to the right with magnetic field into the page

Upward.

Force direction for an electron in the same scenario as above

Downward.

Force direction for a positive charge moving upward through a magnetic field into the page

To the right.

Force direction for a positive charge moving to the left in a magnetic field upward

Out of the page.

Condition for no force on a positive charge moving through a magnetic field

Motion is parallel to the magnetic field.

Symbol for magnetic field out of the page

•

Symbol for magnetic field into the page

×

Force direction for an electron moving upward through a magnetic field to the right

Into the page.

Force direction for a proton moving upward with magnetic field to the right

Out of the page.

Possible B direction for a charge moving north with magnetic force upward

Out of the page.

Reason for negative charge reversing right-hand rule result

Because the equation multiplies by the negative charge, flipping direction.

Force direction for a proton moving east in a downward magnetic field

South (into page).

Force direction for a proton moving into the page with magnetic field upward

Left.

Proton force direction with downward velocity and left magnetic field

Out of the page.

Force direction for an electron moving right with magnetic field upward

Into the page (reverse of proton).

Right-hand rule

Point your fingers in the direction of velocity (v), curl them toward the direction of magnetic field (B), and your thumb points in the direction of the magnetic force on a positive charge. For a negative charge, reverse the thumb direction.

Magnetic force direction for a proton

Use right-hand rule: fingers → right, curl → up → thumb points out of the page.

Magnetic force direction for an electron

Opposite the proton's direction → into the page.

Force on a charged particle parallel to magnetic field

Force = 0, because v × B = 0 when velocity is parallel or antiparallel to the field.

Force direction for a positive charge moving upward

Fingers → up, curl → into page → thumb points right.

Force direction for an electron moving left

Find positive direction first: v = left, B = into page → force = down. Electron → reverse → up.

Magnetic field direction for upward force

Using right-hand rule: v = north (up on page), F = up (toward top of page): B must be out of the page.

Diagram representation of force direction

• = out of page, × = into page.

Negative charge and right-hand rule

Because the magnetic force formula F = q(v × B) includes charge sign; negative q reverses vector direction.

Force direction for a proton moving east

v = east, B = down → force = south (into page).