Variation of electric field and potential along the axis of a cone

[Physics lover]

Homework Statement

The electric field intensity potential and rate of heat generation per unit length aare E,V and H at a section distant a from left end of a conical shaped conductor connected to a battery of emf E.Find the correct options-:
Options are in attempt at a solution

Relevant Equations

J=sigmaE
V=IR

Options are at the top of page as a) b) c) d)
Answer may more than one.
Now since 'a' is distance from the smaller surface of cone so as we move along the axis area will increase,So current charge density will decrease and as we know J=sigma E,E will decrease,but V will remain constant since V=Er and r is increasing and E decreasing.Now i don't if this is correct or not and further how will i find the relation between H and a and H and E.

 

[haruspex]

Your image misses the X axis label in d).
Please post the text of the question word for word, as another image say. Your precis is a bit vague.
If three quantities V, E and R are related by V=ER where R is increasing and E is decreasing, it does not follow that E is constant. You need to know more precisely how E and R depend on a.

Please post algebraic attempts at how E and V vary with a, perhaps as differential equations.

 

[Physics lover]

Your image misses the X axis label in d).
Please post the text of the question word for word, as another image say. Your precis is a bit vague.
If three quantities V, E and R are related by V=ER where R is increasing and E is decreasing, it does not follow that E is constant. You need to know more precisely how E and R depend on a.

Please post algebraic attempts at how E and V vary with a, perhaps as differential equations.

In option d 'a' is on x axis.So how should i proceed further.

 

[Physics lover]

Your image misses the X axis label in d).
Please post the text of the question word for word, as another image say. Your precis is a bit vague.
If three quantities V, E and R are related by V=ER where R is increasing and E is decreasing, it does not follow that E is constant. You need to know more precisely how E and R depend on a.

Please post algebraic attempts at how E and V vary with a, perhaps as differential equations.

Can you tell me which quantity will remain constant as move along axis.Is it I

 

[haruspex]

Can you tell me which quantity will remain constant as move along axis.Is it I

Yes. In any period of time, the flow of charge into a given disc slice of the cone must equal the flow out.

 

[Physics lover]

Yes. In any period of time, the flow of charge into a given disc slice of the cone must equal the flow out.

Ok i think i got it.since I is constant and J is increasing therefore E should increase by J=sigmaE. Am i coorect?

 

[haruspex]

Ok i think i got it.since I is constant and J is increasing therefore E should increase by J=sigmaE. Am i coorect?

I don’t know what J represents in this context, nor what Es are being summed.

 

[Physics lover]

I don’t know what J represents in this context, nor what Es are being summed.

J is current density.and J=sigma E is ohms law.Now can you help please.

 

[haruspex]

J is increasing therefore E should increase by J=sigmaE.

But here you wrote

current charge density will decrease and as we know J=sigma E,E will decrease,

Why have you switched?

 

[Physics lover]

But here you wrote

Why have you switched?

Very sorry for the first one.That was wrong J will decrease as area is increasing isn't it.

 

[Physics lover]

Very sorry for the first one.That was wrong J will decrease as area is increasing isn't it.

Can you please help me further.I could only tell about J and I.

 

[haruspex]

Can you please help me further.I could only tell about J and I.

I think it will help if you are more specific about the algebraic relationship.
Consider a thin disc width da at distance a from the point of the cone. What is its resistance? What is the potential across it? How much power is dissipated in it?