Understanding Electrostatic Potential

Q.

The electric field at 2r from centre of a uniformly charged non conducting sphere of radius r andE .What is the electric field at distance r/2 from centre?

Q.

$1microcoulomb\mu C=$______________.

Q.

Two charges 5 × 10⁻⁸ C and −3 × 10⁻⁸ C are located 16 cm apart. At what point(s) on the line joining the two charges is the electric potential zero? Take the potential at infinity to be zero.

Q. 71.A ball of radius R carries a positive charge whos volume charge density depends on the distance r from the centre of the ball as = [1-r/R]. Find the electric field at distance r>R

Q. Figure shows three concentric thin spherical shells $\text{A, B}$ and $\text{C}$ of radii $R,2R$ and $3R$. The shell $\text{B}$ is earthed and $\text{A}$ and $\text{C}$ are given charges $q$ and $2q$, respectively. Find the charges appearing on all the surfaces of $\text{A, B}$ and $\text{C}$.

1. 
2. 
3. 
4. 

Q. An infinite number of charges, each equal to q, are placed along the x-axis at x =1, x=2, x=8, ... and so on. The potential at the point x =0 due to this set of charges is

1. $\frac{q}{\pi {ϵ}_0}$
2. $\frac{q}{2\pi {ϵ}_0}$
3. $\frac{q}{3\pi {ϵ}_0}$
4. $\frac{q}{4\pi {ϵ}_0}$

Q.

An electric dipole when placed in a uniform electric field E→ will have minimum potential energy, if the positive direction of the dipole make an angle of _____ rad with E→.

1. $\frac{3\pi }{2}$
   
2. 0
3. $\frac{\pi }{2}$
   
4. π

Q. (a) Derive an expression for the electric field E due to a dipole of length '2a' at a point at a distance r from the centre of a dipole on the axial line.
(b) Draw a graph of E versus r for r >> a.
(c) If this dipole was kept in a uniform external electric field $E_0$, diagrammatically represent the position of the dipole in stable and unstable equilibrium and write the expressions for the torque acting on the dipole in both the cases.

Q. A charged particle q is shot towards another charged particle Q which is fixed, with a speed v. It approaches Q upto a closest distance r and then returns. If q were given a speed 2v, the closest distances of approach would be

1. r
2. 2 r
3. $\frac{r}{2}$
4. $\frac{r}{4}$

Q.

Why do two equipotential surfaces never intersect each other?

Q. Electric potential in a particular region of space is $V=12x-3x^{2}y+2y{z}^2$. The magnitude of electric field at point $P(1m,0,-2m)$ in $N/C$ is

Q.

The total flux over a closed surface enclosing the charges q

Q.

The photoelectric cut-off voltage in a certain experiment is 1.5 V. What is the maximum kinetic energy of photoelectrons emitted?

Q.

Let $L$ denote the set of all straight lines in a plane. Let a relation $R$ be defined by $\alpha R\beta \iff \alpha \perp \beta ,\alpha ,\beta \in L.$ Then $R$ is

1. Reflexive

2. Symmetric

3. Transitive

4. None of these

Q.

Any negative charge moves from?

1. \N
2. \N
3. Region of lower potential to higher potential

4. Region of higher potential to lower potential

Q. A charge Q is placed at the centre O of a square ABCD of side a as shown in Fig. 20.15. The work done to move a charge q from A to B is

1. $\frac{qQ}{4\pi {ϵ}_{0}a}$
   
2. $\frac{\sqrt{2}qQ}{4\pi {ϵ}_{0}a}$
3. $\frac{qQ}{2\pi {ϵ}_{0}a}$
4. Zero

Q. A solid non-conducting charged sphere has total charge $Q$ and radius $R$. If energy stored outside the sphere is $V_0$ joules, then find the self energy of the sphere in terms of $V_0$.

1. $\frac{5}{6}{V}_0$
2. $\frac{6}{5}{V}_0$
3. $3V_0$
4. $\frac{V_0}{5}$

Q.

A spherical shell of radius 10 cm is carrying a charge q. if the electric potential at distances 5 cm, 10 cm and 15 cm from the centre of the spherical shell is $V_1,V_{2}and{V}_3$ respectively, then

1. $V_1=V_2>V_3$

2. $V_1>V_2>V_3$

3. $V_1=V_2<V_3$

4. $V_1<V_2<V_3$

Q. a charge q is placed just above the centre of horizontal circle of radius r and hemisphere of the radius is erected about the change compute the electric flux through the closed surface that consist of the hemisphere and the planar circ;e [do not use gauss law]

Q.

Direction of electric field on the equipotential surface is always

1. Parallel to the surface

2. At an angle of 45º to the surface

3. Normal to the surface

4. At an angle of 30º to the surface

Q.

Consider a uniform electric field in the z-direction. The potential is a constant

1. for any x for a given z

2. for any y for a given z

3. on the x-y plane for a given z

4. All of these

Q. A soap bubble of radius r is charged to a potential V. If the radius is increased to n r, the potential on the bubble will become

1. nV
   
2. $\frac{V}{n}$
   
3. $\frac{V}{n^2}$
4. $n^{2}V$
   

Q.

A capacitor is charged to 200 volt has 0.1 coulomb charge when it is discharged energy will be

Q. A particle carrying a charge q is shot with a speed v towards a fixed particle carrying a charge Q. It approaches Q up to a certain distance r and then returns as shown in Fig. 20.12

If charge q were moving with a speed 2v, the distance of the closest approach would be

1. r
2. $\frac{r}{2}$
3. $\frac{r}{8}$
4. $\frac{r}{4}$

Q. A positively charged conductor

1. Is always at +ve potential
2. Is always at zero potential
3. Is always at negative potential
4. May be at +ve, zero or -ve potential

Q.

Why Potential Inside the Conductor is Constant?

Q. A straight wire of length $0.5$ $\text{m}$ and carrying a current of $1.2$ ampere is placed in uniform magnetic field of induction $2$ Tesla. The magnetic field is perpendicular to the length of the wire. The force on the wire is

1. $1.2$ $\text{N}$
2. $2.4$ $\text{N}$
3. $3.0$ $\text{N}$
4. $2.0$ $\text{N}$
   

Q.

A point charge of magnitude 1µC is fixed at (0, 0, 0). An isolated uncharged spherical conductor is fixed with its centre at (4 cm, 0, 0). What is the potential and the induced electric field at the centre of the sphere? Please also explain why the electric field inside the sphere won't be 0.

Q. Two concentric spherical shells are separated by vacuum. The inner shell has total change $Q$ and radius $r$. The outer shell has total charge $-Q$ and radius $2r$. The potential energy stored in the capacitor is

1. $\frac{Q^2}{8\pi {\epsilon }_{0}r}$
2. $\frac{Q^2}{16\pi {\epsilon }_{0}r}$
3. $\frac{4Q^2}{7\pi {\epsilon }_{0}r}$
4. $\frac{Q^2}{2\pi {\epsilon }_{0}r}$

Q. For the electric field shown in figure, its vector representation will be

1. $\overrightarrow{E}=200\hat{i}-\frac{200}{\sqrt{3}}\hat{j}$
2. $\overrightarrow{E}=100\hat{i}-100\sqrt{3}\hat{j}$
3. $\overrightarrow{E}=\frac{50}{\sqrt{3}}\hat{i}-\frac{100}{\sqrt{3}}\hat{j}$
4. $\overrightarrow{E}=10\hat{i}-5\sqrt{2}\hat{j}$