Cambridge IGCSE Physics 0625 – Force on a Current‑Carrying Conductor
4.5.4 Force on a Current‑Carrying Conductor
Learning Objective
Determine the direction of the magnetic force on beams of charged particles (or on a current‑carrying conductor) when they move through a magnetic field.
Key Concepts
The magnetic force on a single moving charge is given by
\$\mathbf{F}=q\,\mathbf{v}\times\mathbf{B}\$
where \$q\$ is the charge, \$\mathbf{v}\$ the velocity vector and \$\mathbf{B}\$ the magnetic‑field vector.
For a straight conductor of length \$L\$ carrying a current \$I\$, the total force is
\$\mathbf{F}=I\,\mathbf{L}\times\mathbf{B}\$
with \$\mathbf{L}\$ directed along the conventional current (from positive to negative).
The magnitude of the force is
\$F=ILB\sin\theta\$
where \$\theta\$ is the angle between \$\mathbf{L}\$ (or \$\mathbf{v}\$) and \$\mathbf{B}\$.
Direction of the Force – Right‑Hand Rule
To find the direction of \$\mathbf{F}\$ use the right‑hand rule for a positive charge (or conventional current):
Stretch the fingers of your right hand in the direction of the velocity \$\mathbf{v}\$ (or current \$\mathbf{I}\$).
Rotate the hand so that when you bend the fingers they point in the direction of the magnetic field \$\mathbf{B}\$.
Extend the thumb; it points in the direction of the force \$\mathbf{F}\$ on a positive charge.
If the moving charge is negative, the force is opposite to the thumb direction.
Suggested diagram: Right‑hand rule showing \$\mathbf{v}\$, \$\mathbf{B}\$ and \$\mathbf{F}\$.
Summary Table – Determining the Force Direction
Charge / Current
Direction of \$\mathbf{v}\$ (or \$\mathbf{I}\$)
Direction of \$\mathbf{B}\$
Resulting Force \$\mathbf{F}\$
Positive charge / Conventional current
Along \$\mathbf{v}\$ (or \$\mathbf{I}\$)
Into page (or any specified direction)
Given by right‑hand rule (thumb)
Negative charge
Opposite to \$\mathbf{v}\$ (since \$q<0\$)
Same \$\mathbf{B}\$ as above
Opposite to the thumb direction (i.e., reverse of positive case)
Worked Example
Problem: A beam of protons (charge \$+e\$) travels eastward with speed \$v\$ and enters a uniform magnetic field that points vertically upward. Determine the direction of the magnetic force on the protons.
Solution:
Identify vectors:
\$\mathbf{v}\$ : east (to the right on a map).
\$\mathbf{B}\$ : upward (out of the ground).
Apply the right‑hand rule:
Point fingers eastward (direction of \$\mathbf{v}\$).
Rotate wrist so fingers can bend upward – they now point upward.
Thumb points southward (into the page on a typical north‑east‑up diagram).
Since protons are positively charged, the force \$\mathbf{F}\$ is in the direction of the thumb – i.e., toward the south.
Common Misconceptions
Confusing the direction of current with electron flow: The right‑hand rule uses conventional current (positive charge flow). If you work with electron flow, reverse the direction of \$\mathbf{I}\$.
Neglecting the sign of the charge: For negative charges the force is opposite to the thumb direction.
Assuming the force is always perpendicular to the motion: It is perpendicular only when \$\theta = 90^\circ\$. If \$\mathbf{v}\$ is parallel or antiparallel to \$\mathbf{B}\$, the force is zero.
Quick Checklist for Determining Force Direction
Identify the sign of the moving charge (or use conventional current).
Draw the velocity (or current) vector.
Draw the magnetic‑field vector.
Apply the right‑hand rule; note the thumb direction.
If the charge is negative, reverse the thumb direction.
State the final direction of \$\mathbf{F}\$ relative to the diagram.
Summary
The magnetic force on a moving charge or a current‑carrying conductor is given by the vector cross‑product \$q\mathbf{v}\times\mathbf{B}\$ (or \$I\mathbf{L}\times\mathbf{B}\$). The direction is found using the right‑hand rule for positive charges (or conventional current) and reversed for negative charges. Mastery of this rule allows you to predict the motion of particle beams in magnetic fields, a key skill for both IGCSE examinations and practical physics applications.