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Difficulty: MediumMagnetic Force and Electromagnetism

Match each physical scenario or effect involving magnetic forces listed on the left with its corresponding physical characteristic or outcome on the right.

  • Magnetic force on a stationary electric charge placed inside a uniform magnetic fieldExactly zero (F=0F = 0) regardless of the field strength, because force depends on non-zero velocity
  • Trajectory of a charged particle entering a uniform magnetic field perpendicular to the field linesCircular trajectory resulting from a constant magnetic force acting as a centripetal force
  • Interaction force between two long parallel straight conductors carrying electric currents in opposite directionsMutual repulsive force pushing the two conductors apart
  • Spatial orientation of the magnetic force vector relative to the charge's velocity vector and the magnetic field vectorPerpendicular to both the velocity vector and the magnetic field vector

Answer

The correct matches pair stationary charges with zero force; perpendicular entry with circular motion; anti-parallel currents with mutual repulsion; and force direction with mutual perpendicularity to velocity and magnetic field vectors.
Each physical scenario correctly pairs with its corresponding principle: stationary charges experience zero magnetic force; perpendicular charge motion forms a circular orbit; anti-parallel currents produce repulsion; and magnetic force is always mutually perpendicular to velocity and field vectors.

Step-by-Step Solution

1
Evaluate the magnetic force formula for a static charge
Using F=qvBsin⁡θF = qvB\sin\theta, with v=0v = 0, F=0F = 0.
A magnetic field does not exert force on a stationary electric charge.
2
Determine the path of a particle moving perpendicular to a magnetic field
The magnetic force acts continuously at right angles to the velocity vector, providing centripetal acceleration and forming a circular orbit.
A perpendicular force of constant magnitude changes motion direction continuously without altering speed.
3
Apply Ampere's law and the right-hand rule to parallel currents in opposite directions
The magnetic field generated by each wire exerts an outward force on the other, producing repulsion.
Opposite currents create reinforcing field lines between the wires, driving them apart.
4
Analyze vector cross product orientation for magnetic force on a charge
The force vector F⃗\vec{F} is oriented perpendicular to the plane containing vectors v⃗\vec{v} and B⃗\vec{B}.
By definition of vector cross-product F⃗=q(v⃗×B⃗)\vec{F} = q(\vec{v} \times \vec{B}), the resultant vector is orthogonal to both input vectors.

Key Concept

Magnetic Force on Moving Charges and Current-Carrying Conductors
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Topics

Magnetic Force and Electromagnetism

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