Q. 83.6( 5 Votes )

The electric field in a region is directed outward and is proportional to the distance r from the origin. Taking the electric potential at the origin to be zero,
A. it is uniform in the region

B. it is proportional to r

C. it is proportional to r2

D. it increases as one goes away from the origin

Answer :

The field around the origin will be like:



Where the intensity of the field will increase as we will move away from the charge placed at origin (as field is proportional to the distance r from the origin.)


Option (a) is incorrect as the field is not uniform in the region (can be perceived by the given situation and the diagram)


Field is given as:



(where k is some positive constant)


Now,





Option (b) is incorrect since V is not proportional to r.


Option (c) is correct since V is proportional to r.


Option (d) is incorrect. From the expression for V, we can say that the potential decreases as we move away. Alternatively, the field lines always flow from high potential to low potential. Therefore, we can say that the potential decreases with increase in r.

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