Electric Field

Given: A graph of electric potential along the X-axis. We are to choose the correct graph of

electric field strength . Key Concept: Electric field is the negative gradient (slope) of electric potential: - Where the potential decreases linearly, is constant and negative. - Where the slope of increases, becomes more negative. - Where the slope becomes less steep (towards flat), approaches zero. - If slope changes sign, changes sign.

Analyzing the given potential graph: - From left to right, the slope (negative of ) is: - Steep (large negative) - Moderate (less negative) - Flat (zero) - Positive slope (negative ), so field becomes positive So, starts negative, increases toward zero, then becomes positive.

Correct Plot: The electric field graph that starts negative, increases, crosses zero, and becomes positive.

Correct Answer: Option (C):

Step-by-step explanation:

We are given a charge distribution over a quarter of a ring, and we are to calculate the net electric field at the center.

Linear charge density: Let total charge be uniformly distributed over an arc of length .

So, linear charge density is:

Electric field due to an arc element:
Consider a small arc element of angle at angle , then its charge is:

Magnitude of the field due to this element at the center is:

Direction: The electric field vector due to each element makes an angle with the x-axis. Its x-component is:

Total field in x-direction:

Due to symmetry: All y-components cancel out, so only x-component remains.

Final Answer:

Substituting :

Or for format answer:
Answer: