Velocity Filter Explained: Class 12 Physics | Magnetic Effect of Current

The right-hand rule is used to find the direction of the magnetic force on a moving charge. The formula is F = qvB sinθ. To apply the rule: point the palm of your right hand in the direction of the magnetic field (B), extend your fingers in the direction of the velocity (v), and your thumb will point in the direction of the force (F). For positive charges, use the right hand; for negative charges, use the left hand. The three vectors (F, v, B) are mutually perpendicular.

The Lorentz force on a moving charge is given by F = qvB sin(θ), where q is the charge, v is the velocity, B is the magnetic field strength, and θ is the angle between velocity and magnetic field. The force is maximum when the charge moves perpendicular to the magnetic field (θ = 90°) and zero when parallel (θ = 0° or 180°). The direction of the force on a positive charge can be determined using the right-hand rule: point fingers in the velocity direction, curl toward the magnetic field, and the thumb indicates the force direction.

Magnetic fields are generated around permanent magnets and moving electric charges. The magnetic force on a moving charged particle is given by F = qvB sin(θ), where q is charge, v is velocity, B is magnetic field strength, and θ is the angle between velocity and field. Maximum force occurs when motion is perpendicular to the field (θ = 90°, sin(90°) = 1), giving F = qvB. Zero force occurs when motion is parallel to the field (θ = 0°, sin(0°) = 0). The Lorentz force combines electric and magnetic forces: F_Lorentz = F_Electric + F_Magnetic. Electric force is F = qE (parallel to field lines), while magnetic force is F = qvB sin(θ) (perpendicular to both velocity and field). The right-hand rule determines force direction: point fingers in velocity direction, curl toward magnetic field, thumb points in force direction.

The magnetic Lorentz force is given by the cross product of velocity and magnetic field vectors. The direction is determined using the right-hand rule: point fingers in velocity direction, curl toward magnetic field, thumb indicates force direction on positive charges. For negative charges, the force acts in the opposite direction.

Magnetic force on moving charge: F = qvB sinθ, perpendicular to both velocity and field. Resting charges experience no magnetic force. For positive charges, use Fleming's Left-Hand Rule; for negative charges, reverse direction or use Right-Hand Rule. Cross product rule: fingers from velocity to field, thumb shows force direction (opposite for negative charges).

Velocity and magnetic field vectors are expressed using unit vectors: v = vĵ for motion in y-direction, B = Bî for field in x-direction. Cross products follow cyclic relationships: î × ĵ = k̂, ĵ × k̂ = î, k̂ × î = ĵ. Reversing operand order changes sign: ĵ × î = -k̂. The determinant method calculates cross products using a 3×3 matrix with unit vectors in the first row and vector components in subsequent rows. For v = vĵ and B = Bî, the determinant yields -k̂, confirming ĵ × î = -k̂.

The right-hand rule determines the direction of the cross product between two vectors. To apply it: point your fingers in the direction of the first vector (velocity), then curl them toward the second vector (magnetic field). Your thumb will point in the direction of the resulting vector. For example, when velocity points in the -I direction and magnetic field points in the +J direction, curling fingers from -I to +J makes the thumb point in the -K direction (into the board).

The cross product direction can be clockwise or counterclockwise depending on vector orientation. When vectors are reversed, the cross product direction becomes opposite (negative). The cross product is always perpendicular to the plane containing both input vectors. Understanding these directional properties is crucial for correctly applying the cross product in physics problems involving forces, rotations, and electromagnetic phenomena.

Magnetic fields differ from electric fields—they are only produced by moving charges, not stationary ones. Compasses measure magnetic fields, which exhibit a characteristic curly pattern around moving charges. The magnetic field of a moving charge depends on the vector cross product between the charge's velocity and the position vector to the observation point. A cross product (a × b) produces a vector perpendicular to the plane containing the two input vectors. The magnitude is |a| × |b| × sin(θ), maximum when vectors are perpendicular and zero when parallel. The direction follows the right hand rule: point fingers in the first vector's direction, curl toward the second, and thumb indicates the cross product direction. Order matters: a × b = -(b × a).

The right-hand rule determines magnetic field direction: point index finger along velocity (QV), thumb along magnetic force (FM), and middle finger indicates field direction (B). If middle finger points toward viewer, field is 'sortant' (exiting); if away, field is 'entrant' (entering). For negative charges (electrons), force direction reverses due to negative Q in FM = Q(V × B). For positive charges (protons), force follows standard rule. The palm method offers an alternative: fingers along QV, thumb along FM; seeing palm interior means 'sortant', seeing back means 'entrant'.

Translational equilibrium occurs when the net force on an object is zero, resulting in zero acceleration. In this state, the object may be at rest or moving with constant velocity. The sum of all forces in each direction must be zero for translational equilibrium to be maintained.

Equilibrium requires net force zero (ΣF = 0), meaning objects remain at rest or move with constant velocity. For translational equilibrium, ΣFx = 0 and ΣFy = 0 must both be satisfied. For two forces: equal magnitude, opposite direction, same point, same plane. For three forces: vector sum zero, same point, same plane. For four+ forces: general ΣF = 0 applies. Solve by drawing Free Body Diagrams, defining axes, and setting equations. For angled forces, resolve components using trigonometry (Tcos(θ), Tsin(θ)). Lami's Theorem (P/sin(α) = Q/sin(β) = R/sin(γ)) provides an alternative for three concurrent forces. Three friction types: static friction (f_s) when stationary, maximum static friction (f_s_max = μ_sN) when about to move, and kinetic friction (f_k = μ_kN) when moving at constant velocity. On inclined planes, resolve weight into mg sin(θ) parallel and mg cos(θ) perpendicular. Three conditions: stationary (mg sin(θ) = f_s), about to move (mg sin(θ) = μ_s mg cos(θ)), moving at constant velocity (mg sin(θ) = μ_k mg cos(θ)). The angle for impending motion is θ = arctan(μ_s).

Translational equilibrium occurs when the net force on a body is zero, meaning the body will not accelerate in any direction. The body's center of mass remains stationary. This is also called 'öteleme dengesi' (translational equilibrium).

The condition for translational equilibrium states that the vector sum of all forces acting on a body must be zero. Mathematically, this means ΣF = 0. For a horizontal bar supported at one end, this implies that the upward normal force must equal the total downward weight of the system (P1 + P2 + PB), where P1 and P2 are the weights of objects on each end, and PB is the weight of the bar itself.

Translational equilibrium occurs when the vector sum of all forces acting on an object equals zero. For horizontal surfaces, weight and reaction forces balance directly. On inclined planes, weight must be decomposed into perpendicular and parallel components; the parallel component requires an equilibrating force (friction, human effort, or springs) to prevent sliding. This principle applies universally: stationary objects have balanced forces, moving objects with constant velocity also achieve equilibrium. The concept enables practical applications from holding shopping carts on ramps to calculating vehicle stability on slopes.