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Define magnetic force vector $\vec{F}$
The force exerted on a current-carrying wire or moving charge due to a magnetic field.
Define current $I$ in the context of magnetic forces on wires.
The rate of flow of electric charge through a wire, measured in Amperes (A).
Define length vector $\vec{L}$ of a wire in a magnetic field.
A vector representing the length of the wire segment within the magnetic field; its direction is the same as the current.
Define magnetic field vector $\vec{B}$.
A vector field that describes the magnetic influence of electric currents and magnetic materials.
Define torque $\tau$ on a current loop.
A rotational force that causes a current loop to rotate in a magnetic field.
Define permeability of free space $\mu_0$.
A physical constant that relates the magnetic field to the electric current that produces it; $\mu_0 = 4\pi \times 10^{-7} T \cdot m/A$.
What is the effect of increasing the current in a wire placed in a magnetic field?
The magnetic force on the wire increases proportionally.
What happens when the angle between a current-carrying wire and a magnetic field is 0 degrees?
The magnetic force on the wire is zero.
What is the effect of placing a current-carrying loop in a magnetic field?
The loop experiences a torque, causing it to rotate (unless perfectly aligned with the field).
What happens when two parallel wires carry current in the same direction?
The wires attract each other.
What is the effect of increasing the distance from a long, straight current-carrying wire?
The magnetic field strength decreases.
What happens when a closed loop of wire is placed in a uniform magnetic field?
The net magnetic force on the loop is zero.
What are the key differences between the Right-Hand Rule (RHR) and the Right-Hand Curl Rule (RHCR)?
RHR: Determines force direction on a charge or wire. Thumb = current, Fingers = B-field, Palm = Force. | RHCR: Determines magnetic field direction around a wire. Thumb = current, Fingers curl = B-field.
Compare and contrast the magnetic force on a single moving charge versus the magnetic force on a current-carrying wire.
Single Charge: Force on a single moving charge is given by $\vec{F} = q\vec{v} \times \vec{B}$. | Current-Carrying Wire: Force on a wire is a summation of forces on individual charges, given by $\vec{F} = I \vec{L} \times \vec{B}$.
Differentiate between the net force and net torque on a closed current loop in a uniform magnetic field.
Net Force: Always zero on a closed loop in a uniform B-field because forces cancel out. | Net Torque: Can be non-zero, causing the loop to rotate; depends on the orientation of the loop.
Compare the magnetic field strength near a long straight wire versus the force between two parallel wires.
Magnetic Field: The magnetic field strength decreases with distance ($B = \frac{\mu_0 I}{2 \pi r}$). | Force Between Wires: The force depends on both currents and the distance between them.
Compare the effect of parallel and anti-parallel currents in two adjacent wires.
Parallel Currents: Wires attract each other due to the interaction of their magnetic fields. | Anti-Parallel Currents: Wires repel each other due to the interaction of their magnetic fields.