Predict magnetic force direction and charge reversals

Predict the bend before calculating

A particle enters a magnetic field moving to your right. Does the force point along its motion, toward you, or sideways? Begin with velocity direction 0° and field +1 T. The solid arrow represents velocity. The dashed arrow represents magnetic force. Predict the dashed arrow for a positive charge, then compare the negative-charge case.

The diagrams are separate trials with prescribed identical velocities. The particles do not exert forces on one another in this model. Their opposite forces are therefore not an action–reaction pair. Both hypothetical particles have mass 1.67 × 10⁻²⁷ kg; the negative one is not an electron, whose mass would differ greatly.

Read three directions on a flat screen

Positive x is right, positive y is up, and positive z points out of the screen toward you. The symbol ⊙ represents an arrow tip coming toward you. The symbol ⊗ represents an arrow tail going away. Positive field points out; negative field points in. Field is measured in teslas (T). The direction symbols do not grow with field strength; read the signed slider value.

At 0°, velocity is along +x. At 90°, it is along +y; at 180°, it points left; at 270°, down. The angle control rotates velocity within the page. It does not change the angle between velocity and the magnetic field: these remain perpendicular whenever the field is nonzero. This is why force magnitude remains unchanged when you rotate velocity at fixed field strength.

Capture 0°, 90° and 180° at +1 T. Explain the changing force components with the coordinate axes. Then return to 0° and reverse the field. Predict before inspecting whether reversing both charge and field would cancel or reinforce the reversal.

Use a direction rule with an explicit sign

Magnetic force is F = q(v × B). F, v and B represent force, velocity and magnetic-field vectors. The cross symbol denotes a cross product: a vector perpendicular to both input directions, not ordinary multiplication. For a positive charge, point your right-hand fingers along velocity and curl toward the field direction; your thumb gives the force direction. For a negative charge, reverse that result. Use the axes to check your hand orientation rather than inferring force from the direction a magnet happens to face.

For this page, B has only a z component, so the rule reduces to Fx = q vy Bz and Fy = −q vx Bz. Subscripts name components along the axes. There is no z force here. At 0°, vx = 100,000 m/s and vy = 0. For q = +1.602 × 10⁻¹⁹ C and Bz = +1 T, Fx = 0 and Fy = −1.602 × 10⁻¹⁴ N, or −16.020 fN. A femtonewton (fN) is 10⁻¹⁵ newtons. The positive charge is forced down; the negative case is forced up.

At 30°, vx is about 86,603 m/s and vy = 50,000 m/s. The positive force is approximately (8.010, −13.874) fN. Its magnitude is still 16.020 fN: components are signed projections, not independent extra forces. The solid velocity arrows and dashed force arrows have different units and separate stated scales. Their lengths should not be compared as if velocity and force were the same quantity.

Distinguish field, motion and force

At 0°, doubling field from +1 to +2 T doubles force magnitude to 32.040 fN while keeping its direction. Reversing field alone reverses force; reversing charge alone also reverses it. Reversing both restores the original force. At B = 0, no magnetic-force arrow is drawn: zero force has no direction. The velocity remains nonzero.

The general magnitude is |F| = |q| v |B| sin θ, where θ is the angle between velocity and field, v is speed and vertical bars denote magnitude. Here θ is always 90° when B is nonzero, so sin θ = 1. The slider angle is measured from +x, not θ. A particle moving parallel to B would feel no magnetic force, but that motion points into or out of this page and is outside the controls. A stationary charge also has zero magnetic force; that does not mean the field is absent. An electric force, if present, would be a separate contribution.

Transfer beyond the controls

A charge of +3.0 × 10⁻¹⁹ C travels at 20,000 m/s along +y in a 0.40 T field along −z. Predict the force magnitude and direction. Then change only the charge sign. Finally consider motion parallel to −z at the same speed.

Check the magnetic-force transfer

The perpendicular case has magnitude 3.0 × 10⁻¹⁹ × 20,000 × 0.40 = 2.4 × 10⁻¹⁵ N = 2.4 fN. Positive charge feels force along −x; negative charge feels force along +x. Motion parallel to the field has zero magnetic force. The last case is a reasoning transfer, not a setting available in the planar browser.

Use a capture to explain a reversal, distinguish the two angle definitions, and identify one condition that would invalidate a magnetic-only force prediction. Field-source response, collisions and electric forces are not included. The diagrams show instantaneous vectors rather than measured tracks.

Reference for the vector law: OpenStax: magnetic fields and lines. The control comparisons and transfer case are original.