Section 9.7: Magnets and Magnetic Field
Magnets produce magnetic fields, which exert forces on other magnets and moving charges. Key concepts include magnetic poles, field lines, and magnetic flux density (B).
Magnetic Force on a Moving Charge:
\[ \vec{F} = q \vec{v} \times \vec{B} \]
where:
\(q\) = charge (C), \(v\) = velocity (m/s), \(B\) = magnetic flux density (T)
\[ \vec{F} = q \vec{v} \times \vec{B} \]
where:
\(q\) = charge (C), \(v\) = velocity (m/s), \(B\) = magnetic flux density (T)
Magnetic Force on a Current-Carrying Conductor:
\[ \vec{F} = I \vec{L} \times \vec{B} \]
where:
\(I\) = current (A), \(L\) = length of conductor in the field (m)
\[ \vec{F} = I \vec{L} \times \vec{B} \]
where:
\(I\) = current (A), \(L\) = length of conductor in the field (m)
Magnetic field lines emerge from the north pole and enter the south pole. Field lines never intersect. The density of lines indicates field strength.
Example 1: Force on a Moving Charge
A proton moves with velocity \(2 \times 10^6\ \text{m/s}\) perpendicular to a magnetic field of 0.5 T. Find the magnetic force on the proton.
\( F = q v B = (1.6 \times 10^{-19})(2 \times 10^6)(0.5) = 1.6 \times 10^{-13}\ \text{N} \)
The magnetic force on the proton is \(1.6 \times 10^{-13}\) N.
Practice Problems
- A 2 C charge moves at 3 m/s perpendicular to a 0.1 T magnetic field. Find the force.
- A wire of length 0.5 m carries 4 A current perpendicular to a 0.2 T field. Determine the magnetic force.
- Sketch the magnetic field lines around a bar magnet.
- Explain why a compass needle aligns with Earth’s magnetic field.
- A proton moves at 5 × 10^5 m/s at an angle of 30° to a 0.3 T field. Find the force magnitude.