The figure shows a rectangular solid conductor of edge lengths L , 2 L , and 3 L

Question

The figure shows a rectangular solid conductor of edge lengths L, 2L, and 3L. A potential difference V is to be applied uniformly between pairs of opposite faces of the conductor as in Figure (b).

First V is applied between the left-right faces, then between the top–bottom faces, and then between the front–back faces.

In the following questions, you will be asked to rank these pairs. If multiple pairs rank equally, use the same rank for each, then exclude the intermediate ranking (i.e. if objects A, B, and C must be ranked, and A and B must both be ranked first, the ranking would be A:1, B:1, C:3). If all pairs rank equally, rank each as '1'.

Explanation / Answer

for left right:
R= rho*L/A
I = V/R
= V*A/(rho*l)
current density: I/A = V/(rho*l)
So if l is more, I current density will be less.

L is max for left-right = 3*L
It is third greatest for top-bottom = L
It is second greatest for front-back = 2*L
current density will follow opposite order

So,
ranking current density:
left-right: 3
top-bottom:1
front-back: 2
------------------------------------------------------------------------------------
I = V/R
= V*A/(rho*l)
so,greater A/l ,greater is current.
A/l for left-right = 2L*L / 3L =2/3
A/l for top-bottom= 2*3L/L = 6
A/l for front-back = L*3L/2L = 3/2

So,
ranking in order of current:
left-right: 3
top-bottom:1
front-back: 2

---------------------------------------------------------------------------
E = v/l
so if l is more E will be less

L is max for left-right = 3*L
It is third greatest for top-bottom = L
It is second greatest for front-back = 2*L
current density will follow opposite order

So,
ranking E
left-right: 3
top-bottom:1
front-back: 2

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