Electric Charges and Fields

Assertion:  An electric field is preferred in comparison to magnetic field for detecting the electron beam in a television picture tube. 

Reason:  Electric field requires low voltage.

• If both assertion and reason are true and reason is the correct explanation of assertion.

• If both assertion and reason are true but reason is not the correct explanation of assertion

• If assertion is true but reason is false.

• If both assertion and reason are false.

Four charges arc arranged at the corners of a square as shown in the figure. The direction of electric field at the centre of the square is along

• DC

• BC

• AB

• AD

Electric field at the centre of a uniformly charged semicircle of radius a is

• $\frac{\mathrm{\lambda }}{2{\mathrm{\pi \epsilon }}_0{\mathrm{a}}^2}$

• $\frac{\mathrm{\lambda }}{4 {\mathrm{\pi }}^2{\mathrm{\epsilon }}_0 {\mathrm{a}}^2}$

• $\frac{{\mathrm{\lambda }}^2}{2{\mathrm{\pi \epsilon }}_0\mathrm{a}}$

• $\frac{\mathrm{\lambda }}{2{\mathrm{\pi \epsilon }}_0\mathrm{a}}$

Two  changes  +q  and  -q  are  attached  to  the  two ends of  a  light rod of length L, as shown in figure. The system is given a velocity  ν  perpendicular to magnetic  field  $\overrightarrow{\mathrm{B}}$. The magnetic force on the system of  charges and magnitude of force on one charge by the rod, are respectively

• zero, zero

• zero, qvB

• 2qvB, 0

• 2qvB,  qvB

A charge q is uniformly distributed on a ring of radius r. A sphere of an equal radius is constructed with its centre lying on the periphery of the ring. The flux of electric field through the surface of the sphere will be

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

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

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

• $\frac{\mathrm{q}}{4{\mathrm{\epsilon }}_0}$

In a case of infinite long wire electric field is proportional to

• $\frac{1}{\mathrm{r}}$

• $\frac{1}{{\mathrm{r}}^2}$

• $\frac{1}{{\mathrm{r}}^3}$

• r⁰

Assertion: In a cavity within a conductor, the electric field is zero.

Reason: Charges in a conductor reside only at its surface.

• If both assertion and reason are true and reason is the correct explanation of assertion

• If both assertion and reason are true but reason is not the correct explanation of assertion

• If assertion is true but reason is false

• If both assertion and reason are false

Two parallel large thin metal sheets have equal surface charge densities ( σ = 26.4 × 10^-12 C/m² ) of opposite signs. The electric field between these sheets is

• 1.5 N/C

• 1.5 × 10^-10 N/C

• 3 N/C

• 3 × 10^-10 N/C 

The spatial distribution of the electric field due to two charges (A, B) is shown in figure. Which one of the following statements is correct?

• A is +ve and +B is -ve and $\left|\mathrm{A}\right| > \left|\mathrm{B}\right|$

• A is $-$ve and B is +ve; $\left|\mathrm{A}\right| = \left|\mathrm{B}\right|$

• both are +ve but A > B

• both are $-$ve but A > B

Using mass (M), length (L), time (T ) and current (A) as fundamental quantities, the dimension of permeability is

• [ M^-1 L T^-2 A ]

• [ M L² T^-2 A^-1 ]

• [ M L T^-2A^-2 ]

• [ M L T^-1 A^-1 ]