Work Done Questions

Charges $+q$ and $-q$ are placed at points $A$ and $B$, respectively; distance $2L$ apart. $C$ is the midpoint. The work done in moving a charge $+Q$ along the semicircle $CRD$ is:

A particle of mass $m$, charge $Q$, and kinetic energy $T$ enters a transverse uniform magnetic field of induction $\vec{B}$. After $3$ seconds, the kinetic energy of the particle will be:

A bar magnet having a magnetic moment of $2\times 10^4{\text{JT}}^{-1}$ is free to rotate in a horizontal plane. A horizontal magnetic field $B=6\times 10^{-4}\text{T}$ exists in the space. The work done in taking the magnet slowly from a direction parallel to the field to a direction $60^{\circ }$ from the field is:

Charges $+q$ are at corners of isosceles $\Delta ABC$ (sides $BC=AC=2a$). $D,E$ are midpoints of $BC,CA$. Work done in moving $Q$ from $D$ to $E$ is:

A uniform force of $(3\hat{i}+\hat{j})\text{N}$ acts on a particle of mass $2\text{kg}$. Hence the particle is displaced from position $(2\hat{i}+\hat{k})\text{m}$ to position $(4\hat{i}+3\hat{j}-\hat{k})\text{m}$. The work done by the force on the particle is:

A gas is taken through the cycle $A\to B\to C\to A$, where $A=(2,2\times 10^5)$, $B=(2,6\times 10^5)$, and $C=(7,2\times 10^5)$ in $(V,P)$ coordinates ($V$ in $10^{-3}{\text{m}}^3$, $P$ in $\text{Pa}$). What is the net work done by the gas?