Understanding Electrostatic Potential Energy

Q. Work done by the field of fixed static charges on a 50mC charge is -20 J, as the charge moves from point A to point B slowly. The work done by the external agent is?

1. 20 J
2. -20 J
3. 100 mJ
4. Zero

Q. Charges $q_1$ and $q_2$, 1C each are at infinite distance from each other initially. They are then brought to 1m distance in vacuum. What was the initial potential energy of the system?

1. None of these.
2. 
3. 
4. 

Q. A capacitor of capacitance $50\text{pF}$ is charged by $100\text{V}$ source. It is then connected to another uncharged identical capacitor. Electrostatic energy loss in the process is $x\text{nJ}$. Find the value of $x$.

Q.

Change in Potential energy is a __________ quantity.

1. Scalar

2. Vector

Q. Electric force on a point charge ‘q’ moving from point A to B is given by $\overrightarrow{F}=4i-8j$. What is the work done by this force if the vector joining A & B is given by $\overrightarrow{AB}=-4i$.

1. -4i + 8j
2. -16i + 32j
3. i – 2j
4. None of these

Q.

A particle of mass m and charge q is released from rest in a uniform electric field E. The kinetic energy attained by the particle after moving a distance x along the electric field is

1. $qE{x}^2$

2. $q{E}^{2}x$

3. $qEx$

4. $q^{2}Ex$

Q. Four particles of mass 1 kg, 2 kg, 2 kg, 3 kg are kept at points A, B, C, D respectively. (All coordinates are in metres)

Choose the correct option(s) regarding the position coordinates (x, y) of the system’s centre of mass.
द्रव्यमान 1 kg, 2 kg, 2 kg, 3 kg के चार कणों को बिन्दुओं क्रमशः A, B, C, D पर रखा गया है। (सभी निर्देशांक मीटर में हैं)
निकाय के द्रव्यमान केन्द्र के स्थिति निर्देशांकों (x, y) के संदर्भ में सही विकल्प/विकल्पों का चयन कीजिए।

1. x = 1.25 m
2. x = 1 m
3. y = 1 m
4. y = 1.25 m

Q. The displacement of a charge Q in the electric field $E=e_1\hat{i}+e_2\hat{j}+e_3\hat{k}$ is $\hat{r}=a\hat{i}+b\hat{j}$. The work done is

1. $Q(a{e}_1+b{e}_2)$
2. $Q\sqrt{(a{e}_1{)}^2+(b{e}_2{)}^2}$
3. $Q(e_1+e_2)\sqrt{a^2+b^2}$
4. $Q\left(\sqrt{e_1^2+e_2^2}\right)(a+b)$

Q. When a +ve q charge is taken from lower potential to a higher potential point, then its PE will

1. Decrease
2. Increases
3. Remain unchanged
4. Become zero

Q. Charges $q_1$ and $q_2$, 1C each are at infinite distance from each other initially. They are then brought to 1m distance in vacuum. What was the initial potential energy of the system?

1. $0$
2. $9\times {10}^9$
3. $-9\times {10}^9$
4. None of these.