General properties of fields

(A) concept of field

A field is a concept introduced to describe a region under the influence of some physical agency such as gravitation, electricity, magnetism, heat etc. There are two kinds of fields which are vector and scalar. Scalar fields include distribution of temperature, density, electric potential, etc. Vector fields include the distribution of velocity in a fluid, gravitational force field, magnetic and electric field.

Note: scalar fields are usually mapped by lines of isothermals, lines of equidensity and lines of equipotential surfaces, while vector fields require magnitude and direction to specify them are usually mapped by lines of influx or lines of force.

Law of gravitational field

The force of attraction between two given particles of masses, M and m is inversely proportional to the square of their distance,r, apart and directly proportional to the product of their masses.

       F_g = GMm/ r²

Where G= the gravitational constant expressed in Nm²kg^-2 .

At the surface of the earth, the force of attraction on a mass ,m, is mg, where g is the acceleration of free fall. If we assume that the earth is a sphere of radius, r, so that the mass of the earth, M, is concentrated at the center, then the force of attraction of the earth on the mass m at the surface is given as. GMm  = mg/ r²

If F_g , is the gravitational force acting at a point where a test charge of mass m is placed then the field g is given by,

           g= F_g / m

From the equation above, the magnitude of the gravitational field g at any point where a test mass m is placed at a distance, r, from mass, M, is given by g= f_g /r² = GMm/ r² = GM/r²

g= GMm/r²

A current carry conductor

Source: www.commons.wikimedia.org 

Electric force and field

Coulomb’s law states in a given medium the force of attraction or repulsion F_g between two bodies with charges of Q and q is directly proportional to the charges and inversely proportional to the square of their separation r. F_e = 1/4π£₀ .  Qq/ r²

The constant proportionality 1/4π£₀ has been chosen to have the value 9.05×10⁹mf^-1.

Electric field

E= F_e / q

The unit of E is Newton/coulomb NC^-1

Since F_e = 1/4π£₀ . Qq/ r² , the magnitude of 

E is given by E= Q/4π£₀r²

Note that F_e is a vector and q is a scalar, so the direction of E is the same as that of F_e which implies that the direction in which a test positive charge placed at the point would tend to move.

Magnetic field

Diagram.

B=F_m / q_m v sinO

Where O is the angle between v and B, while B is the point in terms of F_m , v and q_m. The SI unit of B is the Tesla.

(B) Properties of electric lines of forces

It was discovered by Faraday as an aid in visualizing electric, magnetic and even gravitational fields.

Source: www.physics-and-radio-electronics.com 

Equipotential surfaces

An equipotential surface is a surface on which all points are at the same potential.

Source: www.google.com 

Past questions

1.The following are examples of vector fields except

A. Gravitational force

B. Electric potential

C. Magnetic field

D. Electric field

Answer: B

Solution: electric potential only has magnitude but no direction

2.The following are scalar fields except

A. Density distribution

B. Electric field

C. Electric potential

D. Temperature distribution

Answer: B

Solution: electric has both magnitude and direction

3.Defined equipotential surfaces?

Answer and solution: it can be defined as a surface on which all points are at the same potential.

4. State the law of coulomb

Answer and solution: it states that in a given medium the force of attraction or repulsion F_g between two bodies with charges of Q and q is directly proportional to the charges and inversely proportional to the square of their separation r.

5. At different locations on the Earth’s surface, the Earth’s magnetic field is? (Jamb 1995)

A. The same in magnitude and direction

B. The same in magnitude but different in direction

C. Different in both magnitude and direction

D. Different in magnitude but not in direction

Answer: A