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Motion in Electromagnetic Fields (DP IB Physics)

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  • What is the force on a current-carrying wire in a magnetic field of flux density, B?

    The magnetic force on a current-carrying wire is: F space equals space B I L space sin space theta

    Where:

    • B = magnetic flux density (T)

    • I = current in the wire (A)

    • L = length of the wire in the field (m)

    • theta = angle between the wire and field (°)

  • Name three ways the magnitude of the force on a current-carrying conductor can be increased.

    The magnitude of the force on a current-carrying conductor can be increased by:

    • increasing the strength of the magnetic field

    • increasing the current flowing through the conductor

    • increasing the length of the conductor in the field

  • True or False?

    A current-carrying conductor in a magnetic field will experience a maximum force when the current flows perpendicular to the field.

    True.

    A current-carrying conductor in a magnetic field will experience a maximum force when the current flows perpendicular to the field.

  • What is the force on a current-carrying conductor in a magnetic field when the current flows parallel to the field?

    When the current flows parallel to the magnetic field, the force on the conductor is zero.

  • What is Fleming's left-hand rule?

    Fleming's left-hand rule is used to predict the direction of the magnetic force on a moving charge, or current in a wire, where:

    • thumb = direction of force (motion)

    • first finger = direction of magnetic field (north to south)

    • second finger = direction of current (flow of positive charge)

    Hand demonstrating Fleming's left-hand rule. Thumb indicates motion/force, first finger indicates magnetic field, and second finger indicates current.

  • What is the direction of the magnetic force when current flows from X to Y?

    Diagram showing a wire carrying current between points X and Y, between the poles of a magnet. The magnet's south (S) pole is above the wire and the north (N) pole is below the wire.

    When the current flows from X to Y, the magnetic force is directed upwards according to Fleming's left-hand rule:

    The diagram shows Fleming's left-hand rule with thumb (force), first finger (field), and second finger (current) and a wire carrying current from point X to Y, between the poles of a magnet. The direction of the field is shown from the north to south pole and the force on the wire is directed upwards.

  • What is the direction of the magnetic force when current flows from Y to X?

    A wire carrying current between points X and Y, between the poles of a magnet. The magnet's south (S) pole is above the wire and the north (N) pole is below the wire.

    When the current flows from Y to X, the magnetic force is directed downwards according to Fleming's left-hand rule:

    Fleming's left-hand rule with the thumb (force), first finger (field), and second finger (current) and a wire carrying current from point Y to X, between the poles of a magnet. The direction of the field is shown from the north to south pole and the force on the wire is directed downwards.

  • What two symbols are used to represent a magnetic field directed into or out of the plane of a page?

    The symbols used to represent a magnetic field are dots and crosses, where

    • dots represent a magnetic field directed out of the plane of the page

    • crosses represent a magnetic field directed into the plane of the page

    The left image shows that dots represent a field directed out of the page. The right image shows that crosses represent a field directed into the page.

  • True or False?

    Fleming's left-hand rule is used to determine the direction of the magnetic field around a long straight current-carrying wire.

    False.

    The right-hand grip rule is used to determine the direction of the magnetic field around a long straight current-carrying wire.

  • When the currents in two parallel conductors flow in the same direction, is the force between them attractive or repulsive?

    When the currents in two parallel conductors flow in the same direction, the force between them is attractive.

  • When the currents in two parallel conductors flow in opposite directions, is the force between them attractive or repulsive?

    When the currents in two parallel conductors flow in opposite directions, the force between them is repulsive.

  • Draw the magnetic field lines around two currents flowing in the same direction

    Two identical symbols of a circle with a cross inside represent currents directed into the page.

    The magnetic field lines around two currents flowing in the same direction:

    The magnetic field lines around two currents which are both directed into the plane of the page. Two concentric circles around each current. Two joining circles are joined beyond this.

  • Draw the magnetic field lines around two currents flowing in opposite directions

    Two symbols: on the left is a circle with a dot inside representing a current directed out of the page and on the right is a circle with a cross inside representing a current directed into the page.

    The magnetic field lines around two currents flowing in opposite directions:

    The magnetic field lines around two currents where the one on the left is directed out of the page and the one on the right is directed into the page.

  • What is the force per unit length between two parallel currents, I subscript 1and I subscript 2?

    The force per unit length between two parallel currents is: F over L space equals space mu subscript 0 fraction numerator I subscript 1 I subscript 2 over denominator 2 straight pi r end fraction

    Where:

    • mu subscript 0 = the magnetic permeability of free space (4Ï€ × 10−7 N A−2)

    • I subscript 1 = the current in one conductor (A)

    • I subscript 2 = the current in the other conductor (A)

    • r = the distance between the currents (m)

  • What is the force on a charge moving in a magnetic field of flux density, B?

    The magnetic force on a moving charge is: F space equals space B q v space sin space theta

    Where:

    • B = magnetic flux density (T)

    • q = charge of the particle (C)

    • v = speed of the particle (m s-1)

    • theta = angle between the particle's motion and field (°)

  • True or False?

    A charged particle experiences a maximum force when it travels parallel to a magnetic field.

    False.

    A charged particle experiences a maximum force when it travels perpendicular to a magnetic field.

  • How can the direction of the force experienced by an electron in a magnetic field be determined?

    The direction of the force experienced by an electron in a magnetic field can be determined using Fleming's left-hand rule.

    The second finger (representing the flow of positive current) points in the opposite direction to its motion.

  • True or False?

    In a uniform field, an electron experiences a force perpendicular to the direction of the magnetic field.

    True.

    The force experienced by a moving charge is always perpendicular to the direction of the magnetic field.

  • True or False?

    In a uniform magnetic field directed from left to right, a stationary proton experiences a downward force.

    False.

    If the charge is stationary, it does not experience a force in a magnetic field.

  • Describe the motion of a charged particle in a magnetic field.

    A charged particle in a magnetic field moves in a circular path.

    This is because the magnetic force is always perpendicular to its motion.

  • What is the radius, r, of the path of a charged particle in a perpendicular magnetic field?

    The radius of the path of a charged particle in a magnetic field is: r space equals space fraction numerator m v over denominator B q end fraction

    Where:

    • m = mass of the particle (kg)

    • v = velocity of the charge (m s−1)

    • B = magnetic field strength (T)

    • q = charge of the particle (C)

  • How is the equation for the radius, r, of the path of a charged particle in a magnetic field derived?

    The radius of the path of a charged particle in a magnetic field is derived by equating the centripetal force and the magnetic force on the moving charged particle:

    • F space equals space fraction numerator m v squared over denominator r end fraction space equals space B q v

    • r space equals space fraction numerator m v over denominator B q end fraction

  • How would the path of a charged particle moving in a magnetic field change if the magnetic field strength is increased?

    If the magnetic field strength is increased, the path of the charged particle becomes more curved, i.e. radius decreases as r space proportional to space 1 over B

  • How would the path of a charged particle moving in a magnetic field change if it travels at a greater speed?

    If the particle travels at a greater speed, its path becomes less curved, i.e. radius increases as r space proportional to space v

  • Describe the motion of a stationary charged particle in a uniform electric field.

    A stationary charged particle in a uniform electric field will move parallel to the field lines.

  • Describe the motion of a charged particle in a perpendicularly orientated uniform electric field.

    A charged particle moving perpendicular to a uniform electric field will follow a parabolic path.

  • Sketch the path of the positive charge between the metal plates.

    Two parallel plates with a positive charge to the left. The top plate is positively charged, and the bottom plate is negatively charged

    The positive charge follows a parabolic path towards the negative plate:

    A positive charge moves in a parabolic path between two parallel plates with positive charges on the top plate and negative charges on the bottom plate. The path curves downward to show the charge is attracted towards the negative plate.

  • Sketch the path of the negative charge between the metal plates.

    Two parallel plates with a negative charge to the left. The top plate is positively charged, and the bottom plate is negatively charged

    The negative charge follows a parabolic path towards the positive plate:

    A negative charge moves in a parabolic path between two parallel plates with positive charges on the top plate and negative charges on the bottom plate. The path curves upward to show the charge is attracted towards the positive plate.

  • What three factors affect the amount of deflection of a charged particle in a uniform electric field?

    The amount of deflection of a charged particle in a magnetic field depends on:

    • the mass of the particle

    • the magnitude of the charge of the particle

    • the speed of the particle

  • True or False?

    A heavier particle will deflect more than a lighter particle with the same charge.

    False.

    The greater the mass, the smaller the deflection. Therefore, a heavier particle will deflect less than a lighter particle with the same charge.

    This means it travels a greater horizontal distance before hitting the plate.

  • True or False?

    A Fe2+ ion will deflect more than a Fe3+ ion.

    True.

    The greater the charge, the greater the deflection. Therefore, a Fe2+ ion will deflect more than a Fe3+ ion.

    This means it travels a smaller horizontal distance before hitting the plate.

  • True or False?

    A fast-moving electron will deflect less than a slow-moving electron.

    True.

    The greater the speed, the smaller the deflection. Therefore, a fast-moving electron will deflect less than a slow-moving electron.

    This means it travels a greater horizontal distance before hitting the plate.

  • How can a charged particle moving at a constant speed in perpendicularly orientated uniform electric and magnetic fields continue to move in a straight line?

    A charged particle will continue to move at a constant speed in a straight line if the electric and magnetic forces acting on it are equal and opposite.

  • If a magnetic field is directed into the page and an electron moves horizontally from left to right, in which direction must the electric field be orientated to maintain the electron's motion?

    To maintain the electron's motion, the electric field must be orientated downwards (vertically down the page)

    • The magnetic force acts downwards (according to Fleming's left-hand rule)

    • Therefore, the electric force must act upwards

    • This can be achieved if the electric field is directed downwards

  • If an electric field is directed vertically up the page and a proton moves horizontally from left to right, in which direction must the magnetic field be orientated to maintain the proton's motion?

    To maintain the proton's motion, the magnetic field must be orientated out of the page

    • The electric force acts downwards

    • Therefore, the magnetic force must act upwards

    • This can be achieved if the magnetic field is directed out of the page (according to Fleming's left-hand rule)

  • What is the speed, v, of a charged particle moving in perpendicularly orientated uniform electric and magnetic fields?

    The speed of a charged particle moving in perpendicularly orientated uniform electric and magnetic fields is: v space equals space E over B

    Where:

    • E = electric field strength (N C-1)

    • B = magnetic flux density (T)

  • How is the equation for the speed, v, of a charged particle moving in perpendicularly orientated uniform electric and magnetic fields derived?

    The speed of a charged particle moving in perpendicularly orientated uniform electric and magnetic fields is derived by equating the electric force and magnetic force on the charged particle q E space equals space B q v

    Where:

    • q = charge on the particle (C)

    • E = electric field strength (N C-1)

    • B = magnetic flux density (T)

    • v = speed of the particle (m s-1)

  • What is the charge-to-mass ratio of a particle?

    The charge-to-mass ratio of a particle is the total charge of a particle divided by its total mass.

  • True or False?

    In a magnetic field of strength, B, all particles with the same charge-to-mass ratio, q over m, will follow paths of equal radius, r.

    False.

    The radius of a charged particle in a magnetic field is: r space equals space fraction numerator m v over denominator q B end fraction

    Therefore, to follow paths of equal radius, all particles must have the same velocity, v, as well as the same charge-to-mass ratio, q over m.

  • What four quantities are required to determine a particle's charge-to-mass ratio experimentally?

    To determine a particle's charge-to-mass ratio experimentally, the four quantities required are:

    • the potential difference between the parallel plates, V

    • the separation of the parallel plates, d

    • the magnetic field strength, B

    • the radius of the particle's path in the magnetic field, r (when the electric field is switched off)

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