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Difficulty: HardMagnetic Force and Electromagnetism

Match each physical phenomenon or calculation involving magnetic forces on the left with its corresponding rule, equation, or physical principle on the right.

  • Determining the direction of the magnetic force exerted on a positively charged particle moving through a magnetic fieldFleming's Left-Hand Rule (where thumb indicates thrust/force, forefinger indicates magnetic field, and middle finger indicates conventional current/positive velocity)
  • Determining the pattern and direction of magnetic field lines surrounding a straight current-carrying wireRight-Hand Grip Rule (where thumb points in the direction of conventional current and wrapped fingers show magnetic field direction)
  • Calculating the radius of curvature for a high-speed ion moving perpendicularly to a uniform magnetic fieldEquilibrium between magnetic Lorentz force and centripetal force (r=mvqBr = \frac{mv}{qB})
  • Calculating the attractive force per unit length between two parallel conductors carrying currents in the same directionAmpere's force law between parallel currents (FL=μ0I1I22πd\frac{F}{L} = \frac{\mu_0 I_1 I_2}{2\pi d})

Answer

1 matches with Fleming's Left-Hand Rule; 2 matches with the Right-Hand Grip Rule; 3 matches with the ratio r=mvqBr = \frac{mv}{qB}; 4 matches with the parallel current interaction law FL=μ0I1I22πd\frac{F}{L} = \frac{\mu_0 I_1 I_2}{2\pi d}.
Each electromagnetic phenomenon correctly aligns with its governing physical rule or formula: force direction on a moving charge is determined by Fleming's Left-Hand Rule, magnetic field orientation around a wire by the Right-Hand Grip Rule, circular orbital radius by balancing magnetic force with centripetal force (r=mvqBr = \frac{mv}{qB}), and force between parallel conductors by Ampere's force law.

Step-by-Step Solution

1
Identify the directional rule for magnetic force on a moving charge.
Magnetic force direction is perpendicular to both particle velocity and magnetic field, given by Fleming's Left-Hand Rule.
Fleming's Left-Hand Rule relates thrust/force (thumb), magnetic field (forefinger), and current/positive charge motion (middle finger).
2
Identify the field mapping rule for a current-carrying wire.
Concentric magnetic field lines around a straight wire are mapped using the Right-Hand Grip Rule.
Pointing the right thumb along conventional current causes fingers to curl in the direction of the magnetic field vector.
3
Derive the trajectory equation for a charge in a magnetic field.
Equating magnetic force qvBqvB to centripetal force mv2r\frac{mv^2}{r} yields r=mvqBr = \frac{mv}{qB}.
Because the magnetic force acts as a pure centripetal force, the charge follows a circular trajectory of fixed radius rr.
4
Identify the force law between parallel currents.
The attractive force per length is given by FL=μ0I1I22πd\frac{F}{L} = \frac{\mu_0 I_1 I_2}{2\pi d}.
Current I1I_1 sets up a magnetic field B1=μ0I12πdB_1 = \frac{\mu_0 I_1}{2\pi d} at wire 2, producing force per length B1I2B_1 I_2.

Key Concept

Magnetic Force and Electromagnetism Rules and Equations
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Topics

Magnetic Force and Electromagnetism

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