# SPH4U Grade 12 Physics Gravitational, Electric, and Magnetic Fields Test

Grade 12 Physics – Gravitational, Electric, and Magnetic Fields

Electric Charge

Laws of Electric Charges Opposite charges attract each other. Similar charges repel each other. Charged objects attract some neutral objects.

• Charging by Friction Electrons are ripped off another surface and charges another object
• Ability to rip electrons are based on their position on the electrostatic series
• Induced Charge Separation distribution of charge that results from a change in the distribution of elections in an object
• Charging by Contact Electrons are passed through conductors once they touch. They are transferred and charge equalize each object.
• Charging by Induction The electrons in one object are pushed by the fields of a nearby charged object inducing it.

Law of Conservation of change: The total charge (the difference between the amounts of positive and negative charge) within an isolated system is conserved.

Electric Forces: Coulomb’s Law

• Coulomb’s Law The force between two point charges is inversely proportional to the square of the distance between the charges and directly proportional to the product of the charges

FE = kq1q2 / r2

Where k = 9.0 x 109 N*m2/C2

Electric Fields

• Field of Force: A field of force in a region of space when an appropriate object placed at any point in the field experienced a force.
• Coulombs is a unit measuring the magnitude of charges.

ε = kq1 / r2

• Electric Field: at any point is defined as the electric force per unit positive charge and is a vector quantity.
• Electric Field lines always come from positive to negative charges
• Positive Fields never touch negative fields, they also never crossed

Electric Potential

• Electric Potential Energy (EE) the energy stored in a system of two charges a distance r apart.

EE = kq1q2 / r

• Electric Potential (V), the value, in volts, of potential energy per unit of positive charge. 1 V = 1 J/C

V = kq1 / r

• Electric Potential Difference: the amount of work required per unit charge to move a positive charge from one point to another in the prescience of another field.

ΔV = εr

ε = ΔV / r  (for parallel plates)

ΔV = ΔEE / q

Milikan Experiment: Determining the Elementary Charge

• Through a series of experiments, Milikan found out that the smallest unit of electric charge, called the elementary charge, e, of which other units are simple multiples; e = 1.602 X 10-19 C

Motion of Charged Particles in Electric Fields

• Using electric force formulas, and Newton’s laws of motion we learned in earlier units, we can derive acceleration and include mass to solve motion problems.

a = FE / m

Magnetic Fields

• Magnetic Force Field: the area around a magnet which magnetic forces are exerted.
• Domain Theory of Magnetism: theory that describes, in terms of tiny magnetically homogeneous regions (“domains”), how a material can become magnetized: each domain acts like a bar magnet.
• Principle of Electromagnetism: Moving electric charges produce a magnetic field

• Right hand Rule for a Straight conductor: If a conductor is grasped in the right hand, with the thump pointing in the direction of the current, the curled fingers point in the direction of the magnetic field lines.
• Current flowing through a conductor produces a magnetic field that circles around the conductor based on the direction of the current
• Right hand used for positive charges, left hand used for negative charges

• Right Hand Rule for a Solenoid: If a solenoid is grasped in the right hand, with the fingers curled in the direction of the electric current, the thumb points in the direction of the magnetic field lines in its core.
• A solenoid flowing with current creates a magnetic field that points out of one end of the solenoid
• Relative Magnetic Permeability: the ability for some material to become magnetized

Magnetic Force on Moving Charges

• Force of Magnetic Fields: the force from a magnetic field on a charge moving nearby in the field

FM = qvB sinθ

• Right Hand rule for the direction of magnetic force: Hand flat palm up, thumb at a 90 degree angle to the fingers, where fingers pointed in the direction of the magnetic fields, thumb pointed in the direction of speed of the charge, and palm points outwards to the direction of the magnetic force
• Forces act in perpendicular to the magnetic field lines
• When 2 magnetic plates with poles placed in parallel are there, a charge traveling through will enter circular motion between the plates due to this force

FM = FC , evB = mv2 / r  (since sin 90 degrees = 1)

Magnetic Force on a conductor

• Right hand rule for the motor principle: If the right thumb points in the direction of the current (flow of positive charge), and the extended fingers point in the direction of the magnetic field, the force is in the direction in which the right palm pushes.
• When current flowed from a conductor, within a magnetic field, it has the ability to move due to the interference with the two magnetic fields.

F = I l B sin θ

Ampere’s Law

• Ampere’s Law: Along any closed path through a magnetic field, the sum of the products of the scalar component of the magnetic field (B), parallel to the path segment with the length of the segment, is directly proportional to the net electric current passing through the area enclosed by the path.

B = μo ( I / 2π r)

• Where μo is called the permeability of free space = 4π X 10-7 T*m/A
• For conductors which were a solenoid, a slightly modified formula, based on the total length of wire and number of turns is used

B = μo ( N I / L )

Electromagnetic Induction

• Lenz’ Law: When a current is induced in a coil by changing a magnetic field, the electric current is in such a direction that its own magnetic field opposes the change that it produces
• When applying Right/Left hand rules, the force is opposed and it’s opposite from the field applied