A conductor is made of an isotropic material and has of a truncated cone. A battery of constant emf E is connected across it and its left end is earthed as shown in figure. If at a section distance x from left end, electric field intensity, potential and the rate of generation of heat per unit length are E, V and H respectively, which of the following graphs are correct?
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
(b, c)
Let radius of the conductor at left end be a. Then radius r at distance 'x' from the left end will be given by r = (a + αx), where α is a constant. We know E = i. l/A or E µ 
.
∴ E ∝ 
Hence, curve between E and x will not be a straight line. Therefore, the option is wrong.
H = 
. Hence, H ∝ 
or, H ∝ 
It means, when x increases, H decreases. H will become zero when x is very large and x = 0, H has a finite value. Therefore, the curve between H and x will be as shown in the option . So, the option is correct.
From above two equations
H = i . E
But i is constant, so, H ∝ E. Hence, the curve between H and E will be a straight line having non-zero values at x = 0. Hence, option is also correct.
We know that E = – 
∴ dV = – Edx = – 
dx
Integrating,
= – 
or, V = – 
Hence, at x = 0, V = 0 and V is never +ve. Therefore, the option is wrong.
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems