Fields and Forces

• 6.1.1 State Newton’s Law of gravitation

• 6.1.2 Define gravitational field strength

• 6.1.3 Determine the gravitational field due to one or more point masses.

• 6.2.4 State Coulomb’s Law.

• 6.2.5 Define electric field strength

• 6.2.6 Determine the electric field strength due to one or more point charges.

Forces and Fields

• Newton’s universal law of gravitation– G=6.667 x 10 -11 N m2 kg-2

– Gravitational field strength, g• Unit mass, m• Vector nature, always attractive force

• Coulomb’s law– k= 8.99 x 109 N m2 C-2

– Electric field, E• Unit charge, q (positive)• Vector nature, attractive or repulsive

Forces and Fields

• 6.1.5 Solve problems involving gravitational forces and fields.

• 6.2.8 Solve problems involving electric charges, forces and fields.

• A star explodes and loses half its mass. Its radius becomes half as large. Find the new gravitational field strength on the surface of the star in terms of the original one.

Forces and Fields

• Point P is halfway between the centers of two equal spherical masses (m= 3x1022 kg) that are separated by a distance of 2x109 m. Point Q is located 109m, directly south of Point P. What is the gravitational field strength at Points P and Q?

Forces and Fields

• For an object in centripetal motion orbiting a larger mass, use the universal gravitation law to derive the expression T2=(42R3)/GM

• Two equal charges q are suspended from strings as drawn on the board. Show that tan = (kq2)/mgr2 .

(Remember sin/cos= tan)

Forces and Fields

• 6.1.4 Derive an expression for gravitational field strength at the surface of a planet, assuming that all its mass is concentrated at its center.– Neptune– Jupiter

Forces and Fields

• 6.2.7 Draw the electric field patterns for different charge configurations.

• 6.2.1 State that there are two types of electric charge.

• 6.2.2 State and apply the law of conservation of charge.

• 6.2.3 Describe and explain the difference in the electrical properties of conductors and insulators.

Forces and Fields

• Draw the field lines for the following charges– One positive charge– One negative charge– Two equal positive charges– One negative charge and a positive charge

with twice the magnitude

Forces and Fields

• Electric charging– Friction

• Which particles are transferred?

– Induction• A negatively charged rod is brought near two touching

neutral conductors. What is the charge on each conductor when they’re separated?

– Conduction• Two separated identical conducting spheres with charges of

4C and -12C are allowed to touch and then separated. What’s the charge on each sphere?

Forces and Fields

• 6.3.1 State that moving charges give rise to magnetic fields.

• 6.3.2 Draw magnetic field patterns due to currents.• 6.3.3Determine the direction of the force on a current-

carrying conductor in a magnetic field.• 6.3.4 Determine the direction of the force on a charge

moving in a magnetic field.• 6.3.5 Define the magnitude and direction of a magnetic

field.• 6.3.6 Solve problems involving magnetic forces, fields,

and currents.

Forces and Fields

• Permanent and Temporary magnets

• Right hand rule for magnetic fields– Straight wire– Flat circular coil– Solenoid

• Right hand rule for Force on charges in magnetic field

Forces and Fields

• Calculating Force– F = BILsin– F = qvBsin

• Derive expression for the centripetal motion of charged particles.

• Magnetic Field, B– Direction determined by a “North test

pole”– Vector– Unit of measurement: Tesla

Forces and Fields

• A current I=15A is directed along the positive x axis and perpendicularly to a magnetic field. The conductor experiences a magnetic force per unit length of 0.12 N/m in the negative y direction. Calculate the magnitude and direction of the magnetic field in the region through which the current passes.

• A wire carries a steady current of 2.40A. A straight section of the wire is 0.750m long and lies along the x axis within a uniform magnetic field of magnitude 1.60 T in the positive z direction. If the current is in the +x direction, what is the magnitude of the force on the section of wire?

Forces and Fields

• A proton is moving in a circular orbit of radius 14 cm in a uniform magnetic field of magnitude 0.35 T, directed perpendicularly to the velocity of the proton. Find the orbital speed of the proton.

• A particle of +2.0mC charge and a kinetic energy of 0.090 J is fired into a uniform magnetic field of magnitude 0.10 T. IF the particle moves in a circular path of radius 3.0m, determine the mass.