Electromagnetism Physics - Moving Charges and Magnetism

Apply the right hand palm rule: extend your right hand, thumb points in the current direction, fingers toward the magnetic field B, and the palm indicates the force direction.

Explore magnetic fields from circular loops in different planes, including perpendicular and tilted cases, and the resultant field via B1, B2, and theta. Note when the center field vanishes.

Explain how to compute the center magnetic field of current arcs and loops, using angular dependence and concentric turns, including opposite-direction sign changes.

Apply the right-hand rule to a circular coil carrying current to find the magnetic field direction; when current reverses, the center field remains uniform, forming a two-pole arrangement.

Apply Fleming's left-hand rule to determine the force on a current-carrying conductor: align your left-hand fingers mutually perpendicular, force finger for magnetic field, middle finger for current, thumb for force.

Visualize the magnetic field around a long straight current carrying conductor as concentric circles formed by iron filings and a deflected compass, strongest near the wire and weakening with distance.

Explore magnetic induction produced by a long straight current-carrying wire at distance r, deriving finite- and infinite-length expressions and noting zero induction for points on the axis.

Explore how a cyclotron uses two magnets, a magnetic field and an alternating electric field to accelerate positive charges in a circular path, revealing construction, operation, and size-related limitations.

The radius in a cyclotron is r = m v /(q B), from equating magnetic and centripetal forces; radius grows with mass and velocity and shrinks with charge and field.

Derives the time for a charged particle to complete a circular path in a cyclotron, giving t = 2π m /(q B) and f = q B /(2π m).

Compute the time for a charge to move in a semicircular path inside a cyclotron by relating velocity to radius in a magnetic field, yielding half the circular period.

Explore how a cyclotron yields maximum kinetic energy by equating magnetic and centripetal forces, deriving v_max = q B r / m and E_k,max = q^2 B^2 r^2/(2 m).

Derive the magnetic field from a current element using Biot-Savart's law and integrate along the conductor to obtain the total field at any point.

Ampere's law links magnetic field around a current-carrying conductor to the current, showing that the closed-loop line integral of B · dl equals the permeability of free space times I.

Explore the first application of Ampere's law: magnetic induction at a point from a long straight current, using a circular amperian loop to derive B = μ0 I /(2π r).

Apply Ampere's law to find magnetic induction for solid and hollow cylinders, yielding B inside solid: μ0 I r/(2π R^2), and B inside hollow: μ0 I (r^2−R1^2)/(2π r (R2^2−R1^2)).

Apply Ampere's law with a rectangular loop to derive the center magnetic induction of a solenoid, yielding a uniform interior field B = μ0 n I and zero outside.

Build a toroid by joining the ends of a solenoid into a doughnut-shaped core, confining magnetic induction inside. Apply Ampere's law to show field is tangential inside and zero outside.

Explore Helmholtz coils: two coaxial coils with equal radii and centers separated by one radius, carrying currents in the same direction to produce the resultant magnetic induction at the center.

The moving coil galvanometer detects very small currents, showing needle deflection and current direction on a scale, and cannot handle large currents without burning, prompting ammeter construction.

Explore the construction and working of the moving coil galvanometer, including a cylindrical coil, soft iron core, phosphor bronze winding, magnets, spring, and mirror; derive current, sensitivity, and accuracy.

Derive the current through a moving coil galvanometer by equating deflecting torque NbI with restoring torque Cθ, showing I ∝ θ and yielding I = (C / NB) θ.

this lecture defines current sensitivity of a moving coil galvanometer as the rate of current change with deflection, proportional to turns, area, and magnetic field, and inversely to spring constant.

Derive the accuracy criterion for a moving coil galvanometer by relating current to deflection, showing di/I = dphi/phi from differentiating and dividing the equations to reflect current sensitivity.

The Oersted experiment shows that current through a straight conductor generates a magnetic field that deflects a compass, and reversing or stopping the current reverses or stops the deflection.