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Fields & Effects

 

Electrostatic Fields 2

 

field diagrams

hollow objects

deflection of beams

Van de Graaf

gold leaf electroscope

 

 

 

Electrostatic Field Diagrams

 

 

direction of an electric field

 

 

Electric field direction at a point is the direction of a small free moving positive charge

 

if placed at the point.

 

 

Point Charge Electric Field Patterns:

 

 

electric fields around points

 

 

NB Notice the similarity of the patterns with single magnetic poles.

 

 

Common solid conductor shapes and their field patterns:

 

 

electric field patterns around solid objects

 

 

Observe how the field lines are not evenly distributed over each surface.

 

The charge density σ (sigma) is the amount of charge per unit area. As might be expected, the field strength E at a point is directly proportional to σ (Gauss's theorem).

 

NB Notice how E and σ are higher where the surfaces are highly curved.

 

 

Uniform Electric Field:

 

Two oppositely charged and parallel metal plates(X & Y) will produce a uniform electric field E between them.

 

Note, at the edges the field lines are not evenly spaced. So the field there is not uniform.

 

 

uniform electric field

 

 

The potential difference between the plates is constant along their length.

 

The potential gradient (the drop in pd with distance) is the electric field strength E.

 

Since the pd V and the plate separation d are constant, E is also constant.

 

electric field strength for a uniform electric field

 

Lines of the same potential are called equipotentials . These are placed at right angles to the electric field lines.

 

As a result of the field being uniform, the equipotential lines are equally spaced.

 

 

E-V relation, equipotentials

 

 

 

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Fields in and around hollow objects

 

The simplest case is of a sphere.

 

outside of the sphere : E and V are the same as for a point charge at the sphere centre.

 

inside the sphere : E is zero in the material of the shell and in the enclosed space, while V is constant throughout (VC).

 

 

E and V for a hollow sphere

 

 

 

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Deflection of Ion Beams

 

From our definition of field strength (E=F/Q) , making the force F the subject of the equation, for a small charge q related to a particle :

 

ion deflection - equation #1

 

 

ion deflection by an electric field

 

 

This force is constant at right angles to the original velocity v.

 

The vertical displacement Sy of the particle can be found from one of the 'equations of motion' used in mechanics :

 

ion deflection - equation #2

 

where,

 

u is the original velocity, in this case u = 0
t is the period of acceleration
a is the acceleration

 

 

Substituting for u ,

 

ion deflection - equation #3

 

From Newton's 2nd Law of Motion,

 

ion deflection - equation #4

 

Elimenating F , using our original expression for field strength,

 

ion deflection - equation #5

 

Rearranging to make the acceleration a the subject,

 

ion deflection - equation #6

 

Returning to the expression for vertical displacement and substituting for a ,

 

ion deflection - equation #7

 

The expression for horizontal displacement SX can be rearranged to give an expression for t .

 

ion deflection - equation #8

 

By substituting for t into the Sy equation we obtain our final expression :

 

ion deflection - equation #9

 

ion deflection - equation #10

 

The equation is of the form y = kx2 , where k is a constant. The curve of the function is therefore a parabola.

 

 

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Van de Graaf Generator

 

The Van de Graaf generator is a machine for producing extremely high potential differences (>107 V).

 

 

Van der Graaf generator

 

 

At the bottom (A), positive ionised air molecules are created at the points of a metal 'comb'. The molecules repel and are 'sprayed' onto the rubber belt.

 

The belt in turn takes the charges up to another comb (B). Here the charges induce negative charges which spread over the inside of the sphere.

 

Positive charge is induced on the outside of the sphere.

 

At the same time, negative charges from the inside of the sphere are sprayed onto the belt to neutralise the positive ones.

 

As the belt rotates more positive charge is taken up to the sphere and the cycle repeats itself.

 

 

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Gold Leaf Electroscope

 

The Gold Leaf Electroscope is a simple device but effective in the following areas:

 

i) measuring electrical potential

 

ii) detecting the presence of charge close to it

 

iii) determining whether a charge is positive or negative

 

 

 

the gold-leaf electroscope

 

 

The two gold leaves are freely suspended and diverge when charged. The degree of divergence is a measure of the charge imparted.

 

 

 

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