Electric Force and Electric field

Electric Force and Electric field

1. There are two types of electric charge (positive and negative)


2. Static charges can be produced by the action of friction on an insulator

Electric force and electric field

3. Conductors contain many free electrons inside them (electrons not associated with one particular atom)


4. Charge is conserved. The total charge of an isolated system cannot change.

I’m indestructible!

So am I!

Coulomb’s law

F = kq1q2

r2

The constant k is sometimes written as

k = 1/4πεo

where εo is called the permittivity of free space.

Calculations using Coulomb’s law

The force between two charges is 20.0 N. If one charge is doubled, the other charge tripled, and the distance between them is halved, what is the resultant force between them?

q1q2

r

r/2

2q1 3q2

F = 20N

F = ? N

Calculations using Coulomb’s law

F = kq1q2/r2 = 20.0N

x = k2q13q2/(r/2)2 = 6kq1q2/(r2/4) = 24kq1q2/r2

x = 24F = 24 x 20.0 = 480 Nq1

q2

r

r/2

2q1 3q2

F = 20.0N

x = 480 N

Electric field

An area or region where a charge feels a force is called an electric field.

The electric field strength at any point in space is defined as the force per unit charge (on a small positive test charge) at that point.

E = F/q (in N.C-1)

Electric field around a point charge

If we have two charges q1 and q2 distance r apart

F = kq1q2/r2

Looking at the force on q1 due to q2, F = Eq1

F = kq1q2/r2 = Eq1

E (field due to q2) = kq2/r2

q1 q2

NOT in data book

Electric field

Electric field is a vector, and any calculations regarding fields (especially involving adding the fields from more than one charge) must use vector addition.

q1 q2

Resultant field

Field due to q1

Field due to q2

Electric field patterns

An electric field can be represented by lines and arrows on a diagram , in a similar ways to magnetic field lines.

The closer the lines are together, the stronger the force felt.This is an

example of a radial field

Field around a charged metal sphere

E = 0 inside the sphere

Field around two point charges

Field between charged parallel plates

Uniform field E = V/dV

d

“Edge effects”

NOT in data book

Remember!

The force F on a charge q in a field E is

F = Eq

Gravitational Force and Field

We already know that;

1. Masses attract each other


We will know that;

2. Mass/energy is conserved

(E = mc2)


The force between masses was formulated (discovered?) by Isaac Newton in 1687

Newton’s law of universal gravitation

F = Gm1m2

r2

The constant G is known as “Big G” and is equal to 6.667 x 10-11 Nm2kg-2

Newton’s law of universal gravitation

F = Gm1m2

r2

For large objects like the earth, r is the distance to the centre of mass

Calculations using Newton’s law

What is the force of attraction between Pascal and Chris?

2 m

63kg ? 70kg ?

Calculations using Newton’s law

F = Gm1m2 = 6.667 x 10-11 x 63 x 70 = 7.3 x 10-8 N

r2 22

2 m

63kg ? 70kg ?

Force of gravity due to earth on Pascal?

F = Gm1m2 = 6.667 x 10-11 x 63 x 6 x 1024 = 615 N (= mg)

r2 (6400 x 103)2

63kg ?

R = 6400 km, m = 6 x 1024 kg

Pascal’s weight

Force of gravity due to earth on Pascal?

F = Gm1m2 = 6.667 x 10-11 x 63 x 6 x 1024 = 615 N (= mg)

r2 (6400 x 103)2

In other words, for any planet;

g = Gmp

rp2

Gravitational field

An area or region where a mass feels a gravitational force is called a gravitational field.

The gravitational field strength at any point in space is defined as the force per unit mass (on a small test mass) at that point.

g = F/m (in N.kg-1)

Gravitational field around a point mass

If we have two masses m1 and m2 distance r apart

F = Gm1m2/r2

Looking at the force on m1 due to m2, F = gm1

F = Gm1m2/r2 = gm1

g (field due to m2) = Gm2/r2

m1 m2

Gravitational field around a point mass

If we have two masses m1 and m2 distance r apart

F = Gm1m2/r2

Looking at the force on m1 due to m2, F = gm1

F = Gm1m2/r2 = gm1

g (field due to m2) = Gm2/r2

m1 m2

I told you, for any planet;

g = Gmp

rp2

Don’t forget that for a non point mass, r is the

distance to the centre of mass

Gravitational field

Gravitational field is a vector, and any calculations regarding fields (especially involving adding the fields from more than one mass) must use vector addition.

m1 m2

Field due to m1

Field due to m2

Resultant Field

Gravitational field patterns

A gravitational field can be represented by lines and arrows on a diagram, in a similar ways to magnetic field lines.

Gravitational field patterns

A gravitational field can be represented by lines and arrows on a diagram, in a similar ways to magnetic field lines.

This is an example of a radial field

The closer the lines are together, the stronger the force felt.

Note, gravity is ALWAYS attractive

Field around a uniform spherical mass

Field close to the earth’s surface

Uniform

ALL magnets have two poles

NORTH seeking pole

SOUTH seeking pole

Opposite poles attract and like poles repel

Magnetic materials

Iron (steel), Cobalt and Nickel

Magnetic induction

When a magnetic material is close to a magnet, it becomes a magnet itself

We say it has induced magnetism

NS

NSmagnet

Soft Magnetism

Pure iron is a soft magnetic material

It is easy to magnetise but loses its magnetism easily

NS

before after

Iron nail

SN

NS

Not a magnet

N

Hard Magnetism

Steel is a hard magnetic material

It is harder to magnetise, but keeps its magnetism (it is used to make magnets!)

NS

before after

Steel paper clip

NNS

It’s a magnet!

N

S

S N

Magnetic field

Magnets and electric currents produce magnetic fields around them.

In a magnetic field, another magnet, a magnetic material or a moving charge will experience a magnetic force.

www.physchem.co.za

Magnetic field lines

The closer the field lines are, the stronger the magnetic force felt

The arrows show the direction a compass needle would point at that point in the field.

Note that magnetic field is a vector quantity

Moving charges (currents)

Moving charges (electric currents) also produce a magnetic field

http://www.sciencebuddies.org

Conventional current – electrons flow in the opposite direction

Magnetic field around a straight wire

Stronger field closer to wire

Magnetic field around a flat circular coil

http://physicsed.buffalostate.edu

Magnetic field around a solenoid

The Motor Effect

When a current is placed in a magnetic field it will experience a force. This is called the motor effect.

The Motor Effect

The direction of the force on a current in a magnetic field is given by Flemming’s left hand rule.

Centre finger = Conventional Current

First finger = Field direction

Thumb = Motion

D.C.Motor

Commutator ensures that every half rotaion the current direction reverses in the coil

Defining Magnetic Field B

The size of the force on a wire in a field depends on the size of the field (B), the length of wire in the field (L) and the current in the wire (I)


In other words , F α BIL, or F = kBIL


F = kBIL

We can make k = 1 by defining the Tesla as the magnetic field when the force on 1 m of wire carrying a current of 1 A is 1 N.

Force on a current in a field

Thus the force on a length L of wire carrying a current I in a magnetic field B is given by F = BILsinθ where θ is the angle between the current and the magnetic field.

The force on a moving charge in a magnetic field

Since a current experiences a force in a magnetic field, and a current is just made of moving charges, moving charges themselves must experience a force in a magnetic field.

www.nearingzero.net


Given that F = BILsinθ

F = B(q/Δt)vΔt = Bvqsinθ

v

q


The fact that this force is always at right angles to the velocity means that the charge will move in a circle (if the speed is constant)

v

qNote; If the force is perpendicular to the motion, no work is done.

Electric Force and Electric field

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