Potential Gradient and Relation between Electric Field and Potential

Q.

Three-point charges q, - 4q, and 2q are placed at the vertices of an equilateral triangle ABC of side 'l' as shown in the figure.

(a)Obtain the expression for the magnitude of the resultant electric force acting on the charge q.

(b) Find out the amount of work done to separate the charges at an infinite distance.

Q. What is an electric dipole?

Q. The electric field in a region is radially outward and is given by $E=250r\text{V/m}$ at a point (where $r$ is the distance of the point from the origin). Calculate the charge contained in a sphere of radius $20\text{cm}$ centred at the origin.

1. $2.22\times {10}^{-6}\text{C}$
2. $2.22\times {10}^{-8}\text{C}$
3. $2.22\times {10}^{-10}\text{C}$
4. Zero

Q. The electric field intensity at points $P$ and $Q$ in the shown arrangement, are in the ratio

1. $1:2$
2. $2:1$
3. $1:1$
4. $4:3$

Q. $\text{ABC}$ is an equilateral triangle of side $2\text{m}$. If electric field $E=10{\text{NC}}^{-1}$ then the potential difference $V_A-V_B$ is

1. $10\text{V}$
2. $-10\text{V}$
3. $20\text{V}$
4. $-20\text{V}$

Q.

What is the relation between current density and electric field?

Q. The variation of potential with distance R from a fixed point is as shown below. The electric field at R = 5m is

1. 2.5 volt/m
2. - 2.5 volt/m
3. $\frac{2}{5}$ volt/m
4. $-\frac{2}{5}$ volt/m

Q.

Two-point charges of 2 micro C but opposite in sign are placed 10 cm apart to calculate the electric field at a. Point 10 cm from mid point on the axial line of dipole.

Q. A solid conducting sphere, having a charge $Q$, is surrounded by an uncharged conducting hollow spherical shell. Let the potential difference between the surface of the solid sphere and that of the outer surface of the hollow shell be $V$. If the shell is now given a charge of $-4Q$, the new potential difference between the same two surfaces is

1. $V$
2. $2V$
3. $-2V$
4. $4V$

Q. A non-conducting ring of radius 0.5 m carries a total charge of $1.11\times {10}^{-10}C$ distributed non-uniformly on its circumference producing an electric field $\stackrel{\rightharpoonup }{E}$ everywhere in space. The value of the line integral $-{\int }_{l-\infty }^{l=0}\stackrel{\rightharpoonup }{E}\stackrel{\rightharpoonup }{dl}$ (l=0 being centre of the ring) in volt is

1. + 2
2. - 1
3. - 2
4. Zero

Q. A solid conducting sphere having a charge $Q$ is surrounded by an uncharged concentric conducting hollow spherical shell. Let the potential difference between the surface of the solid sphere and that of the outer surface of the hollow shell be $V$. If the shell is now given a charge $-4Q$, the new potential difference between the same two surfaces is :

1. 4 V
2. 2 V
3. -2 V
4. V

Q. An electric field is given by $\overrightarrow{E}=(y\hat{i}+x\hat{j})\text{N/C}$. The work done in moving a $1\text{C}$ charge from $\overrightarrow{r_A}=(2\hat{i}+2\hat{j})\text{m}$ to $\overrightarrow{r_B}=(4\hat{i}+\hat{j})\text{m}$ is

1. $+4\text{J}$
2. $-4\text{J}$
3. $+8\text{J}$
4. Zero

Q. three charges each +q are placed at the corners of an isosceles triangle ABC of side BC and AC , 2a .D and E are the midpoints of side BC and CA.the work done in taking a charge Q from D toE i

Q. An infinite conducting sheet has surface charge density $\sigma$. The distance between two equipotential surfaces is $r$. The potential difference between these two surfaces is

1. $\frac{\sigma r}{2{\epsilon }_0}$
2. $\frac{\sigma r}{{\epsilon }_0}$
3. $\frac{\sigma }{{\epsilon }_{0}r}$
4. $\frac{\sigma }{2{\epsilon }_{0}r}$

Q.

The electric potential v at any point $(x,y,z)$, all in meters in space is given by $V=4x^{2}V$. The electric field at the point $(1,0,2)$ in volt/meter, is:

1. 8 along negative X-axis

2. 8 along positive X-axis

3. 16 along negative X-axis

4. 16 along positive X-axis

Q. determine the electric field strength vector if the potential of this field depends on x, y coordinates as v=10 axy

Q.

Electric field is always directed from positive to negative. While dipole moment is always directed from negative to positive. So, it seems that dipole moment and electric field should always be in opposite directions. But in questions we come across that dipole moment is inclined at some angle to the direction of electric field. Why?

Q. The electric potential at a point (x, y) in the x - y plane is given by V = - kxy. The field intensity at a distance r from the origin varies as

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

Q.

What happens to the electric current when the potential difference is zero?

Q. Three charges of unequal magnitudes can remain in equilibrium if arranged on a
$[$Assume two charges of same nature$]$

1. circle
2. triangle
3. straight line
4. None of these

Q. There are two charged particles of same nature, and they are fixed.The position of equilibrium for the third charge will be

Q. Statement A: Electric potential may exist at a point where the electric field is zero
Statement B: Electric Field may exist at a point where the electric potential is zero.
Statement C: The electric potential inside a charged conducting sphere is constant.

1. A, B are true
2. B, C are true
3. A, C are true
4. A, B, C are true

Q. In moving from A to B along an electric field line, the electric field does $6.4\times {10}^{-19}J$ of work on an electron. If ${\varphi }_1,{\varphi }_2$ are equipotential surfaces, then the potential difference $(V_C-V_A)$ is?

1. -4V
2. 4V
3. Zero
4. 64V

Q. 31.Two charges Q and -4q are kept at points A& B. The correct variation of v along the AB is

Q. Equilibrium of symmetric geometrical point charged systemValue of Q at centre for which system to be in state of equilibriumoQa.of a equilateral triangle and squarewith each side a and charge on ech vertex q

Q. A charge $+q$ is placed at the centre of the line joining of two exactly equal positive charges $Q$. Charge $q$ can move only in $x-x^{\prime }$ direction as shown in figure. Assume $+Q$ charges to be fixed.

In which of the above cases charge $q$ is in stable equilibrium ?

1. (I) and (II)
2. (II) and (III)
3. (III) and (IV)
4. (I) and (IV)

Q. A uniform electric field of magnitude $E_0$ is directed along the positive X - axis. If the potential V is zero at x = 0, then its value at X = + x will be

1. $V_x=+x^2{E}_0$
2. $V_x=+x{E}_0$
3. $V_x=-x{E}_0$
4. $V_x=-x^2{E}_0$

Q. 28. A solid sphere of radius R is charged uniformly throughout the volume. At what distance from its surface, is the electric potential 1/4 of the potential at the centre?

Q. An electron is taken from point A to point B along the path AB in a uniform electric field of intensity $E=10V{m}^{-1}$. Side AB = 5 m and side BC = 3 m. Then, the amount of work done on electron is

1. $50eV$
2. $40eV$
3. $-50eV$
4. $-40eV$

Q. A charge $Q$ is placed at a distance $L$ from the charge $-2q$ as shown in figure.

The system of three charges will be in equilibrium, if $Q$ is equal to

1. $-4q$
2. $+4q$
3. $+8q$
4. $-8q$