Electric Charges and Fields

If the electric fluxes entering and leaving an enclosed surface respectively are  Φ₁ and Φ_2, the electric charge inside the surface will be

• (Φ₂ − Φ₁) ε₀

• (Φ₁ + Φ₂) / ε₀

• (Φ₂ − Φ₁) / ε₀

• (Φ₁ + Φ₂) / ε₀

Shown below is a distribution of charges. The flux of electric field due to these charges through the surface is

• $\frac{3\mathrm{q}}{{\mathrm{\epsilon }}_0}$

• zero

• $\frac{2\mathrm{q}}{{\mathrm{\epsilon }}_0}$

• $\frac{\mathrm{q}}{{\mathrm{\epsilon }}_0}$

Two point charges + q and + 4q are located at x = O and x = L respectively. The location of a point on the x-axis at which the net electric field due to these two points charges is zero, is

• L / 3

• 2 L

• 4 L

• 8 L

If electric flux entering and leaving an enclosed surface is ${\mathrm{\varphi }}_1$ and ${\mathrm{\varphi }}_2$ respectively, the electric charge inside the enclosed surface will be

• $\left({\mathrm{\varphi }}_1 + {\mathrm{\varphi }}_2\right) {\mathrm{\epsilon }}_0$

• $\left({\mathrm{\varphi }}_2 - {\mathrm{\varphi }}_1\right) {\mathrm{\epsilon }}_0$

• $\left({\mathrm{\varphi }}_1 + {\mathrm{\varphi }}_2\right) / {\mathrm{\epsilon }}_0$

• $\left({\mathrm{\varphi }}_2 - {\mathrm{\varphi }}_1\right) / {\mathrm{\epsilon }}_0$

The electric field in a region is given by E = $\left(4 \stackrel{\wedge }{\mathrm{i}} + 3 \stackrel{\wedge }{\mathrm{j}}\right)$V/m. The net flux passing through a square area of side 4 m parallel to y-z plane is

• 32 V-m

• 16 V-m

• 12 V-m

• 64 V-m

Two concentric conducting spherical shells A and B having radii r_A and r_B (r_B > rA) are charged to Q_A and -Q_B $\left(\left|{\mathrm{Q}}_{\mathrm{B}}\right| > \left|{\mathrm{Q}}_{\mathrm{A}}\right|\right)$ . The electric field along a line passing through the centre is

• $\left|{\mathrm{Q}}_{\mathrm{B}}\right| > \left|{\mathrm{Q}}_{\mathrm{A}}\right|$

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• 

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Two charged spheres separated by a distance d exert some force (F) on each other. If they are immersed in a liquid of dielectric constant 4, then what is the force exerted, if all other conditions are same ?

• 2F

• 4F

• $\frac{\mathrm{F}}{2}$

• $\frac{\mathrm{F}}{4}$

A charge q is located at the centre of a cube. The electric flux through any face is

• $\frac{4\mathrm{\pi q}}{6 \left(4{\mathrm{\pi \epsilon }}_0\right)}$

• $\frac{\mathrm{\pi q}}{6\left(4{\mathrm{\pi \epsilon }}_0\right)}$

• $\frac{\mathrm{q}}{6\left(4{\mathrm{\pi \epsilon }}_0\right)}$

• $\frac{2\mathrm{\pi q}}{6\left(4{\mathrm{\pi \epsilon }}_0\right)}$

An electron enters uniform electric field maintained by parallel plates and of value E Vm^-1 with a velocity v ms^-1 , the plates are separated by a distance d metre, then acceleration of the electron in the field is

• $\frac{\mathrm{Ee}}{\mathrm{m}}$

• $\frac{-\mathrm{Ee}}{\mathrm{m}}$

• $\frac{\mathrm{Ed}}{\mathrm{m}}$

• $\mathrm{Ee}\frac{\mathrm{d}}{\mathrm{m}}$

The electrostatic field due to a charged conductor just outside the conductor is 

• zero and parallel to the surface at every point inside the conductor

• zero and is normal to the surface at every point inside the conductor

• parallel to the surface at every point and zero inside the conductor

• normal to the surface at every point and zero inside the conductor