# 16.25 Electrical charge

Before you read this, I suggest you read posts 16.4 and 16.16.

In post 16.16 we met the concept of a gravitational field. Are there other kinds of fields? Yes – two that we encounter in everyday life are the electric field and the magnetic field. Both arise because some objects can have a property called electrical charge. Electrical charge (sometimes simply called charge) is measured in units called coulombs (abbreviated to C). We are not very familiar with stationary charges in everyday life, but whenever we switch on anything electrical we see the effects of them moving – an electrical current. We measure current by the number of coulombs that flow in one second. You might then expect that current would be measured in coulombs per second (C/s or C.s-1 – see posts 16.12 and 16.13 for more explanation about units) but this unit has a special name – the amp (abbreviated to A). However, charges can also be stationary – a capacitor in an electric circuit is a device for storing charge.

Positively charged objects tend to push each other away – they exert a force of repulsion. This is because a charge q creates an electric field at a distance r from itself whose strength is E = q/(4πεr2). In this equation ε is called the permittivity of the stuff in the space where we are calculating the field. Often ε is written as εr × ε0 where εr is called the relative permittivity (also known as the dielectric constant) for the stuff and ε0 is the permittivity of a vacuum (usually called the permittivity of free space). The value of ε0 is
8.854 × 10-12 m3.kg-1.s4.A2.

If another charge, q’, is placed in this field, it experiences a force of F = q’E.

There can be negative, as well as positive, charges. If q’ has a negative value, F will act in the opposite direction and so q’ is attracted to q.

An electric current produces a magnetic field. For a very long (strictly speaking infinitely long) straight wire with a current, I, flowing in it, the strength of the field at a distance r from the wire is given by B = µI/(2πr). In this equation µ is the permeability of the stuff where we are calculating the field strength. The permeability can be written as µ = µr × µ0 where µr is the called the relative permeability of the stuff and µ0 is called the permeability of free space. The higher the value of the relative permeability, the stronger the field. For iron it has a value of about 5 × 103; for air, water, plastics and copper it has a value of about 1. So, everything else being equal, magnetic fields are about five thousand times stronger in iron than in air. The strength of the magnetic field is measured in units called the tesla (abbreviated to T). The permeability of free space has a value of 4π × 10-7 T.m.A-1. Permanent magnets, for example compass needles, are made of materials that contain moving charges.

Magnetic fields exert a force on a moving charge. The force acting on a charge q moving at a speed v by a magnetic field B is F = Bqv. The force acts at right angles to the direction of the moving charge.

In post 16.4, we saw that whether we consider an object to be stationary or moving at a constant velocity depends on the motion of the observer. Therefore, whether a charge has a magnetic, as well as an electric, field depends on the motion of the observer. If a charge moves in the frame of reference of the observer, the observer is in a magnetic field.

If you have been reading this post carefully, you will have noticed that we don’t yet have a definition of the coulomb (the unit of charge). This is because of the official definition of the amp (the unit of current). Because a moving charge (a current) exerts a force on another moving charge (another current), two wires conducting an electric current will exert a force on each other. If the force between two very long (strictly speaking infinite) parallel wires, of negligible diameter, that are a distance of 1 m apart, in a vacuum, is 2 × 10-7 N, then is current flowing in the wires is defined to be 1 A. The coulomb is then the charge that flows when there is a current of 1 A flowing for 1 s.

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