Q.Define 'electric field' and discuss its various aspects.

Step 1. Definition. The electric field at a point P is the force per unit positive test charge $q_0$ placed there: $\vec{E}=\vec{F}/q_0$.

Step 2. Point-charge field. For a source charge $q$, $\vec{E}=\dfrac{1}{4\pi\varepsilon_0}\dfrac{q}{r^2}\hat{r}$, directed away from $q$ if positive, toward $q$ if negative.

Step 3. Independence from test charge. The test charge $q_0$ is taken vanishingly small so it does not disturb the source; the field itself depends only on the source charge and location.

Step 4. Uniform vs non-uniform. A field is uniform if it has the same magnitude and direction everywhere in a region (e.g. between two oppositely charged infinite sheets); a point charge's field, changing in direction and magnitude from point to point, is non-uniform.

Step 5. Superposition. For several point charges, $\vec{E}_{\text{total}}=\sum_i\vec{E}_i$, the vector sum of each individual contribution.

Step 6. Continuous distributions. For extended charge, the object is divided into infinitesimal elements $dq$, each contributing $d\vec{E}=k\,dq/r^2\,\hat{r}$, summed by integration.

Define E = F/q0, derive the point-charge formula, and discuss uniform/non-uniform fields, superposition, and continuous distributions as the 'various aspects' asked for.

• Presenting only the point-charge formula without discussing superposition or the uniform/non-uniform distinction, both of which the question explicitly asks about.