Rankers Physics
Topic: Electrostatics
Subtopic: Electric Field

As shown in the figure a positive charge +q is placed at x = –a and negative charge –q is placed at x = + a. Then choose the curve which shows variation of E along the x-axis :
none of these

Solution:

The figure represents the electric field (E) along the \(x\)-axis due to a dipole consisting of a positive charge (\(+q\)) at \(x = -a\) and a negative charge (\(-q\)) at \(x = +a\).

The electric field due to such a dipole varies as follows:

1. Near \(x = -a\): The field is dominated by the positive charge, so it points away from \(x = -a\).
2. Near \(x = +a\): The field is dominated by the negative charge, so it points toward \(x = +a\).
3. Between \(x = -a\) and \(x = +a\): The contributions from both charges partially cancel out, leading to a local minimum in the field magnitude.
4. Far from the charges (\(|x| \gg a\)): The field behaves approximately as a dipole field, decreasing as \(1/x^3\).

The attached graph correctly shows these features:
- A local minimum in \(E\) between \(x = -a\) and \(x = +a\), at the midpoint where the dipole effect is weakest.
- The field magnitude diverges near \(x = -a\) and \(x = +a\) due to the proximity to the charges.
- Symmetry around the origin is preserved, as the system is symmetric about \(x = 0\).

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