Which property of a test system does NOT influence the intrinsic electric field vector created by a stationary source charge at a given observation point?
The magnitude of the charge carried by the test particle
The electric field of a source charge is defined as force per unit test charge: \(\vec{E} = \frac{\vec{F}}{q_0} = \frac{1}{4\pi\varepsilon}\frac{Q}{r^2}\hat{r}\).
Doubling the test charge q₀ doubles the force F, so the ratio F/q₀ is unchanged; the field is independent of the test charge’s magnitude (assuming it is small enough not to disturb the source).
The permittivity ε of the medium does affect E, since E is inversely proportional to ε.
The distance r affects E through the inverse-square dependence.
The sign of the source charge Q decides whether the field points away from (positive) or toward (negative) the source, so it changes the field vector.
Hence, the answer is The magnitude of the charge carried by the test particle.
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Important Questions from Electric Fields and Gauss' Law
The surface charge density of a thin spherical shell placed in an air medium is 88.54 c/m2 The intensity of the electric field measured 12 mm outside the shell from the centre of the shell is 5.625 × 101 2 N/C. The thin spherical shell has a radius of:
The electric flux passing through a surface of area A = 8j m2 in an electric field vector E = 2i + 3j - 4k V/m (bold is for vectors) is:
- Let a total charge $2Q$ be distributed in a sphere of radius $R$, with the charge density given by $\rho(r) = Cr^2$, where $r$ is the distance from the centre. Two charges $A$ and $B$, of $-Q$ each, are placed on diametrically opposite points, at equal distance, '$a$' from the centre. If $A$ and $B$ do not experience any force, then:
- Two point charges $q_1 \left( {\sqrt {10} {\rm{\mu C}}} \right)$ and $q_2(-18\sqrt{2} {\rm{\mu C}})$ are placed on the x-axis at $x = 0$ m and $x = 4$ m respectively. The electric field (in V/m) at a point $(1, 3)$ m is,
$\left[ {{\rm{Take\;}}\frac{1}{{4{\rm{\pi }}{\epsilon_0}}} = 9 \times {{10}^9}{\rm{N}}{{\rm{m}}^2}{{\rm{C}}^{ - 2}}} \right]$ The electric field between the two plates of a parallel plate (area = 5.0 × 10-2m2) capacitor is given by E = (2.0 × 105 – 4.0 × 104 t) V/m where t is in second. What is the magnitude of the displacement current between the plates? (ε0 = 8.85 × 10-12 F/m)
