In an electrical circuit, a battery is connected to pass $20\, C$ of charge through it in a certain given time. The potential difference between two plates of the battery is maintained at $15\, V$. The work done by the battery is ........... $J$.

The ratio of momenta of an electron and an $\alpha$-particle which are accelerated from rest by a potential difference of $100\, volts$ is

A point charge $q$ is held at the centre of a circle of radius $r . B, C$ are two points on the circumference of the circle and $A$ is a point outside the circle. If $W_{A B}$ represents work done by electric field in taking a charge $q_0$ from $A$ to $B$ and $W_{A C}$ represents the workdone from $A$ to $C$, then

A test charge $q$ is made to move in the electric field of a point charge $Q$ along two different closed paths as per figure. First path has sections along and perpendicular to lines of electric field. Second path is a rectangular loop of the same area as the first loop. How does the work done compare in the two cases ?

A negative point charge placed at the point $A$ is

As per this diagram a point charge $ + q$ is placed at the origin $O$. Work done in taking another point charge $ - Q$ from the point $A$ [co-ordinates $(0,\,a)$] to another point $B$ [co-ordinates $(a, 0)$] along the straight path $AB$ is