Understanding Electrostatic Potential Energy

Q. A particle of mass $m$ and charge $q$ is in electric and magnetic field given by,
$\overrightarrow{E}=2\hat{i}+3\hat{j},\overrightarrow{B}=4\hat{j}+6\hat{k}.$
The charged particle is shifted from the origin to the point $P(x=1,y=1)$ along a straight path. The magnitude of the total work done is :

1. $5q$
2. $0.15)q$
3. $\left(0.35\right)q$
4. $\left(2.5\right)q$

Q. If the gravitational potential due to the earth at infinite distance from it is zero, the potential at a point $P$ is $-5{\text{J kg}}^{-1}$. Suppose we arbitrarily assume the gravitational potential at infinity to be $+10{\text{J kg}}^{-1}$. Then, gravitational potential at $P$ will be

1. $-5{\text{J kg}}^{-1}$
2. $+5{\text{J kg}}^{-1}$
3. $-15{\text{J kg}}^{-1}$
4. $+15{\text{J kg}}^{-1}$

Q. The potential energy of a particle varies with velocity v, as U= AV^3/v+B where A and B are constants. Dimensional formula of A/B

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.

When a positive charge is moved in an electrostatic field from a point at high potential to a low potential, its kinetic energy________.

Q.

The amount of work done in moving a unit positive charge through a distance of $10\mathrm{cm}$ on an equipotential surface is

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. In the electric field of a fixed point charge $q$, a certain charge is carried from point $A$ to $B,C,D$ and $E$ as shown in the figure. Then the work done :

1. Is least along the path $AB$
2. Is least along the path $AD$
3. Is zero along all the paths
4. Is least along the path $AE$

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.

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. Work done by an electrostatic force in moving a point charge ‘q’ from point A to B is given by $\overrightarrow{W}=4i-8j$. 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. 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. The potential energy of a particle is given as a function of distance x and time t as U = a x upon ( b- t) the dimensional formula of A and b

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

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. 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. Zero
4. 100 mJ

Q. Two charges of equal magnitude 'q' are placed in air at a distance '$2a$' apart and third charge '$-2q$' is placed at midpoint. The potential energy of the system is ________.

1. $-\frac{q^2}{8\pi {ϵ}_{0}a}$
2. $-\frac{5q^2}{8\pi {ϵ}_{0}a}$
3. $-\frac{7q^2}{8\pi {ϵ}_{0}a}$
4. $-\frac{3q^2}{8\pi {ϵ}_{0}a}$

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.

Q. In S.H.M., let the time period of variation of potential energy be T₁ and time period of variation of position be T₂, then relation between T₁ and T₂ is : -
(1) T₁ = T_{2 (2)} T₁ = 2T₂ (3) 2T₁ = T₂ (4) None