Ok i read that the charge (current) entering the conductor is same as that of charge leaving through the conductor Means current is same at all the points in a conductor having varying cross section. My question is how? If the conductor have varying cross section how the current should be same at every point and also at cross sections. After this i want to ask what is the difference between current and current density. And i also study that that current is directly proportional to area. so the current should need to be high at large cross section?
If a wire becomes thicker the current density goes down. Current density is current per unit surface.
Current is only proportional to area at constant current density.
For a start, for a perfect conductor, the current flows on the surface, not in the bulk.
The conservation law is: in = out + accumulated. Any surface separating the source and sink will have a constant flux across it. This is calculated by integrating the dot product of the flux with the surface normal over the surface.
The net current is constant but the current density will vary with geometry.
So lets take a wire of radius r. The circumference (not area) is 2 pi r. Therefore the current density will be proportional to 1/r.
Current density if big enough causes a breakdown in insulation. That is why thicker wires can handle higher currents.
If the conductor have varying cross section how the current should be same
Because current is not a per-area measure.
If I send 10 charges-per-second into a wire, then I don't care if they suddenly have more space if the wire widens somewhere. 10 charges must still enter and leave per second at every point. Otherwise charge would accumulate somewhere.
Think of it as a water pipe system. Send in 10 litres-per-second and you will see 10 liters-per second enter and leave every point along the pipe. If only, say, 8 litres-per-second left some point, then that point would accumulate 2 liters every second. That would soon be a lot of water. The pressure would soon be so large that the out-flowing water would increase to fit the 10 litres-per-second - otherwise you either would at some point not be able to press in any more water or the pipe would break.
Same idea goes for electric circuits and wires. Current is analogous to the water flow rate. It doesn't say anything about the shape or size of pipes / wires along the way, it just says "how much" that flows through per second.
This concept is in general called Kirchhoff's current law, by the way.
what is the difference between current and current density
Current density is the same concept, but with area taken into account. Current density is in fact what you originally thought current was. It is charges flowing per second **per area*.
current is directly proportional to area.
No, this is not true.
Current e.g. provided by a battery may be proportional to other parameters such as resistance in a resistor, and such resistance is proportional to area. But it is not a general rule for current.