A string of length $0.5$ m and mass $10^{-3}$ kg is tightly clamped at its ends. The tension in the string is $0.8$ N. Identical wave pulses are produced at one end at equal intervals of time $\Delta t$. What is the minimum value of $\Delta t$ which allows constructive interference between successive pulses?

Which of the following statements is NOT TRUE?
a. Work done to move a charge on an equipotential surface is not zero.
b. Equipotential surfaces are the surfaces where the potential is constant.
c. Equipotential surfaces for a uniform electric field are parallel and equidistant from each other.
d. Electric field is always perpendicular to an equipotential surface.

Two metal sphere of radius $R$ and $3R$ have same surface charge density $\sigma$. If they are brought in contact and then separated, the surface charge density on smaller and bigger sphere becomes $\sigma_1$ and $\sigma_2$, respectively. The ratio $\dfrac{\sigma_1}{\sigma_2}$ is.

Three charges $q$, $Q$ and $+4q$ are placed in a straight line of length $d$ at points at distance $0$, $\dfrac{d}{3}$, $\dfrac{2d}{3}$ respectively. In order to make the net force on $q$ be zero, the value of $Q$ should be