FIELDS (I.E GRAVITATIONAL FIELDS, ELECTRIC FIELDS)

FIELDS (I.E. GRAVITATIONAL FIELDS, ELECTRIC FIELDS)

Gravitational force between two masses

Gravitation is the force of attractive exerted by a body on all other bodies in the universe. Hence a gravitational force exists between a body and all other bodies around it. Gravitational forces act between all masses and hold together planets, stars, and galaxies. Each mass has a gravitational field around it.

 Newton’s law of Gravitation.

Laws of universal gravitation states that every particle in the universe attracts every other particle with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between them. This force acts along the line joining the centre of the particles.

F =  ; where m1 and m2 are the masses of the two particles, r is the distance between them  and G is a universal constant of gravitation (G = 6.67 x 10-11 Nm2kg-2)

Relationship between Gravitational constant ‘G’ and the acceleration of gravity at the earth surface ‘g’

g =

Gravitational potential

Gravitational potential (V) at a point is defined as the work done in taking unit mass from infinity to that point. Unit is Jkg-1.

V =

Escape velocity

Escape velocity (ve)is defined as the minimum velocity required for an object (e.g satellite or rocket) to just to escape or leave the gravitational influence or field of astronomical body permanently.

Ve =  ; where R is the earth’s radius

Example

Calculate the force of attraction between two small objects of mass 10Kg and 50Kg respectively which are 10cm apart. Take G as 6.67x10-11Nm2Kg-2.

Solution

F =  =  = 3.33x10-6N

Coulomb’s law.

Coulomb’s law stated as the electric force between two point of charges q1 and q2 separated by a distance r is directly proportional to the product of their charges and inversely proportional to the square of the distance between the charges.  F = . K is a proportionality constant, K = ; where £0 is a constant known as permittivity of free space. Its unit  C2N-1m-2. K =  = 9.0x109Nm2C-2.

Electric line of force

Electric line of force are imaginary lines drawn in such a way that the direction at any point (i.e direction of the tangent) is the same as the direction of the field at that point, OR, The line of force is the path which an isolated small positive charge would follow if placed in the field.

Electric field intensity

Electric field intensity or The strength of an electric field, E, at any point is defined as the force per unit positive charge (q) at that point.

E =  . If F is measured in Newtons and q in Coulombs, then the field intensity E is in Newtons per Coulombs (NC-1).

Electric intensity at a point due to several charges is the vector sum of the intensities due to the individual charges.

We can obtain the equation for the Field Intensity E due to a point charge q at a distance r from that charge q at a distance r from that charge. We assume the point charge is situated in vacuum.

 


The force between point charge Q and test charge q situated at B is F =

Field intensity at B is E =  =  =  =  .

 This is the field intensity due to a charge Q at a distance r from the charge.

Electric gravitational potential

The gravitational potential at any point in a gravitational field is the work done per unit mass in bringing mass to that point from an arbitrarily chosen zero level, the ground or sea level of the earth.

Electric Potential (V) at a point is defined as the work done in bringing unit positive charge from infinity to that point against the electrical forces of the field.

Consider two points A and B in an electric field. If more work is done in bringing unit positive charge from infinity to A than to B we say A is at higher potential than B. There is then a potential difference (p.d) between A and B. This difference in potential is equal to the extra work done in moving the positive charge from B to A against the electric field.

Potential difference (VAB) between two points A and B is the work done in taking unit positive charge from one point to the other in the electric field.

Both the potential and the potential difference are scalar quantities having the dimension of work/charge. The unit is volt.

W=qV; V=  

Potential at a point (V) due to a charge q at a distance d from the charge. V =

Example

Find the force of attraction between two equal but opposite charges, of 2 x 10-6 C if the distance between them is 25 cm.

Solution

F =  =  =  = 0.576N

Assignment

1.       Calculate the force per unit mass on the earth’s surface. Take G = 6.67x10-11 Nm2kg-2, mass of the earth = 5.98x1024 kg, and radius of the earth= 6.38x106m.

2.       The plates of a parallel plate capacitor, 5.0x10-3m apart are maintained at a potential difference of 5.0x104V. Calculate the magnitude of the (i) Electric field intensity between the plates (ii) Force on the electron  (iii) Acceleration of the electron. (electronic charge = 1.6 x 10-19C, mass of electron -9.1 x 10-31kg) 

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