Physics Worksheet 3: Magnetic Fields and Forces

Fundamental Definitions and Magnetic Properties

  • Magnetic Field Definition: A magnetic field is best described as the region around a magnet where magnetic forces can act.

  • Magnetic Attraction and Repulsion:

    • Pairs of magnetic poles that attract each other include the North pole and the South pole (unlike poles attract).

    • Pairs of magnetic poles that repel each other include North and North, or South and South (like poles repel).

Magnetic Field Lines and Field Strength

  • Direction of Field Lines: Outside a bar magnet, magnetic field lines always travel from the North pole to the South pole.

  • Location of Maximum Strength: The magnetic field is strongest near the poles of a magnet. This is because the magnetic field is strongest where the field lines are closest together. Around a bar magnet, the field lines are at their highest density near the North and South poles, resulting in the strongest magnetic force in these areas.

Principles of Magnetic Force

  • Force on a Current-Carrying Wire: A current-carrying wire placed at right angles to a magnetic field experiences a force calculated by the formula:     F=BILF = BIL

    • FF represents the magnetic force.

    • BB represents the magnetic field strength (measured in Tesla, TT).

    • II represents the current in the wire (measured in Amperes, AA).

    • LL represents the specific length of the wire that is inside the magnetic field, rather than the total length of the circuit or battery.

  • Force on a Moving Charged Particle: The magnetic force exerted on a moving charged particle is determined using the equation:     F=qvBF = qvB

    • qq represents the magnitude of the charge (measured in Coulombs, CC).

    • vv represents the speed or velocity of the particle (measured in m/sm/s).

    • BB represents the magnetic field strength.

  • The Mechanism of Interaction: A current-carrying wire experiences a force in a magnetic field because the wire produces its own magnetic field. When placed inside an external magnetic field, the two fields interact. This interaction exerts a force on the wire, which is greatest when the wire is perpendicular to the external field line direction.

Directionality and the Right-Hand Rule

  • The Right-Hand Rule (RHR): This method is used to determine the direction of the force on a current-carrying wire or a positive charge. To apply this rule, three factors must be known:

    1. The direction of the conventional current (or the velocity of a positive charge).

    2. The direction of the magnetic field.

    3. The orientation of the wire (it must be at an angle to the field, usually 90∘90^{\circ} for maximum force).

    • Perpendicularity: The resulting force is always perpendicular to both the direction of the current/velocity and the magnetic field.

  • Charged Particles and the Right-Hand Rule:

    • Protons: For a positive charge like a proton, the Right-Hand Rule directly predicts the force direction. For example, if a proton moves to the right through a field directed into the page, the force is directed upward.

    • Electrons: The direction of force on an electron is opposite to the direction predicted by the Right-Hand Rule. Because the Right-Hand Rule applies to positive charges and an electron has a negative charge, the force direction is inverted. If an electron moves to the right through a field directed into the page, the force is directed downward.

Earth's Magnetism and the Compass

  • Function of a Compass: A compass needle is essentially a small magnet. Because the Earth possesses its own magnetic field, the needle aligns itself with Earth's magnetic field lines. The north-seeking end of the compass needle points toward Earth's magnetic north direction.

Worked Numerical Examples

  • Calculating Force on a Wire:

    • Given: Current I=6.0 AI = 6.0\,A, Field Strength B=0.50 TB = 0.50\,T, Length L=0.40 mL = 0.40\,m.

    • Formula: F=BILF = BIL

    • Calculation: F=(0.50)(6.0)(0.40)F = (0.50)(6.0)(0.40)

    • Result: F=1.20 NF = 1.20\,N

  • Finding Current in a Wire:

    • Given: Length L=0.50 mL = 0.50\,m, Field Strength B=0.40 TB = 0.40\,T, Force F=1.60 NF = 1.60\,N.

    • Formula: I=FBLI = \frac{F}{BL}

    • Calculation: I=1.60(0.40)(0.50)=1.600.20I = \frac{1.60}{(0.40)(0.50)} = \frac{1.60}{0.20}

    • Result: I=8.0 AI = 8.0\,A

  • Balancing the Weight of a Wire:

    • Given: Length L=0.30 mL = 0.30\,m, Current I=4.0 AI = 4.0\,A, Weight W=0.24 NW = 0.24\,N.

    • Context: The magnetic force FBF_B balances the weight WW, so FB=W=0.24 NF_B = W = 0.24\,N.

    • Formula: B=FILB = \frac{F}{IL}

    • Calculation: B=0.24(4.0)(0.30)=0.241.20B = \frac{0.24}{(4.0)(0.30)} = \frac{0.24}{1.20}

    • Result: B=0.20 TB = 0.20\,T

  • Force on an Electron:

    • Given: Speed v=4.0×106 m/sv = 4.0 \times 10^6\,m/s, Field Strength B=5.0×10−2 TB = 5.0 \times 10^{-2}\,T, Charge q=1.6×10−19 Cq = 1.6 \times 10^{-19}\,C.

    • Formula: F=qvBF = qvB

    • Calculation: F=(1.6×10−19)(4.0×106)(5.0×10−2)F = (1.6 \times 10^{-19})(4.0 \times 10^6)(5.0 \times 10^{-2})

    • Result: F=3.2×10−14 NF = 3.2 \times 10^{-14}\,N

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