The electric field in a region is directed outward and isproportional to the distance r from the origin.Takingthe electric potential at the origin to be zero,a)it is uniform in the regionb)it is proportional to rc)it is proportional tod)it increases as one goes away from the originCorrect answer is option 'C'. Can you explain this answer?

Question

Answer

Explanation:
The electric field in a region is given as E ∝ r, where r is the distance from the origin. The electric potential at the origin is zero, which means that the electric potential V depends only on the distance r from the origin.

The relation between electric field and electric potential is given as E = -∇V, where ∇ is the gradient operator. Since the electric field is directed outward, the gradient of the electric potential must be negative, i.e., ∇V < />

By integrating the relation between electric field and electric potential, we get V = -∫E.dr, where the integral is taken along the path from infinity to the point r. Substituting the expression for E, we get V = -∫k.r.dr, where k is a constant of proportionality.

Integrating this expression, we get V = -k.r2/2 + C, where C is a constant of integration. Since the electric potential at the origin is zero, we get C = 0. Therefore, the electric potential is given by V = -k.r2/2.

Thus, we see that the electric potential is proportional to r2, which means that option (c) is the correct answer.

Answer

Answer

NYC handwriting

Answer

Hm the ans. C is correct as u known that dE = -(dV/dr) we can neglect the sign and then by rearranging we get dE * dr = dV and so V is directly proportional to E and r and E is proportion to r , so in total V is proportional to r*r i.e. r^2

Answer

As, E=-dV/dX, so dv=Edx. as E propertional to r
on integrating v directly propertional to r^2

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