Potential Gradient and Relation between Electric Field and Potential

Q. The electric potential varies in space according to the relation $V=3x+4y.$ A particle of mass $0.1kg$ starts from rest from point $(2,3.2)$ under the influence of this field. The charge on the particle is $+1\mu C.$ Assume $V$ and $(x,y)$ are in S.I. units
The time taken to cross the $x$ - axis is

1. $20s$
2. $40s$
3. $20s$
4. $400s$

Q. An electron moves on a circular orbit of radius r with constant speed v . The force acting on it is

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. An electric field is expressed as $\overrightarrow{E}=2\hat{i}+3\hat{j}$. Find the potential difference $(V_A-V_B)$ between two points A and B whose position vectors are given by $r_A=\hat{i}+2\hat{j}$ and $r_B=2\hat{i}+\hat{j}+3\hat{k}.$

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

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. There is an electric field E along X-direction. If the work done on moving a charge 0.2 C through a distance of 2m along a line making an angle ${60}^{\circ }$ with the X-axis is 4.0, what is the value of E

1. $\sqrt{3}N/C$
2. 4 N/C
3. 5 N/C
4. None of these

Q. In a region, the potential is represented by $V(x,y,z)=6x-8xy+6yz$, where $V$ is in volts and $x$, $y$ and $z$ are in metres. The electric force experienced by a charge of $2$ Coulomb situated at point $(1,1,1)$ is

1. $6\sqrt{5}N$
2. $30N$
3. $24N$
4. $4\sqrt{35}N$

Q. Two charged spheres of radii 10 cm and 15 cm are connected by a thin wire. No current will flow, if they have

1. The same charge on each
2. The same potential
3. The same energy
4. The same field on their surfaces

Q. If potential in a region of space is given by $V=x^{2}y$, what is the electric field in the region?

1. $\hat{i}+\hat{j}+\hat{k}$
2. $-2xy\hat{i}-x^2\hat{j}$
3. $-x^2\hat{i}-2xy\hat{j}$
4. None of these

Q. A uniform electric field pointing in positive x-direction exists in a region. Let A be the origin, B be the point on the x-axis at x = +1 cm and C be the point on the y-axis at y = +1 cm. Then the potentials at the points A, B and C satisfy:

1. $V_A<V_B$
2. $V_A>V_B$
3. $V_A<V_C$
4. $V_A>V_C$

Q. The electric potential at x=3 on the curve of $y=x^2$is 10V and it is 20 V at a point x= 4 (on the same curve). What is the average potential gradient between these two points?

1. $\frac{2V}{m}$
2. $\frac{\sqrt{5}V}{m}$
3. $\frac{3V}{m}$
4. $\text{None of these}$

Q. The variation of potential with distance $x$ is as shown in figure. The field at $x=6m$ is

1. $-1.5V/m$
2. $+3V/m$
3. $-3V/m$
4. $+1.5V/m$

Q. In a space, potential $\left(V\right)$ is given by $V={\log }_e\left(xy\right)$, where $V,x,y$ are in SI units. The angle between $\overrightarrow{E}$ & $X$-axis at point $(6,6\sqrt{3})\text{m}$

1. ${30}^{\circ }$
2. ${150}^{\circ }$
3. ${210}^{\circ }$
4. ${240}^{\circ }$

Q. Electric potential is given by $V=6x-8x{y}^2-8y+6yz-4z^2$
Then electric force acting on a 2C point charge placed at origin will be?

1. 2 N
2. 6 N
3. 8 N
4. 20 N

Q. If the electric potential along a line due to a charge is given by $V\left(r\right)=\frac{25}{r}+3$, where r is the distance from the charge, what is the electric field at a point r = 5 along this line?

1. $-1\frac{N}{C}$
2. $1\frac{N}{C}$
3. $5\frac{N}{C}$
4. $-5\frac{N}{C}$

Q. In a region, the potential is represented by $V(x,y,z)=6x-8xy-8y+6yz$, where $V$ is in $\text{Volts}$ and $x,y,z$ are in $\text{meters}$. The electric force experienced by a charge of $2\text{coulombs}$ situated at the point $(1,1,1)$ is:-

1. $4\sqrt{35}\text{N}$
2. $30\text{N}$
3. $24\text{N}$
4. $6\sqrt{5}\text{N}$

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. If $\overrightarrow{E}=2\hat{i}-4\hat{j}+3\hat{k}$ find the potential difference between (1, 2, 1)and (-1, 3, 4)

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

Q. The electric potential varies in space according to the relation $V=3x+4y.$ A particle of mass $0.1kg$ starts from rest from point $(2,3.2)$ under the influence of this field. The charge on the particle is $+1\mu C.$ Assume V and $(x,y)$ are in S.I. units
The component of electric field in the y - direction $\left(E_y\right)$ is

1. $3V{m}^{-1}$
2. $-4V{m}^{-1}$
3. $5V{m}^{-1}$
4. $8V{m}^{-1}$

Q. The electric potential varies in space according to the relation $V=3x+4y.$ A particle of mass $0.1kg$ starts from rest from point $(2,3.2)$ under the influence of this field. The charge on the particle is $+1\mu C.$ Assume V and $(x,y)$ are in S.I. units
The component of electric field in the x - direction $\left(E_x\right)$ is

1. $-3V{m}^{-1}$
2. $4V{m}^{-1}$
3. $5V{m}^{-1}$
4. $8V{m}^{-1}$

Q.

If Electric field in a region is given by $E=x^2\hat{i}+y\hat{j}+\hat{k}$. What is the potential of the point (1, 2, 3) given the potential of the origin is 10V?

1. $\frac{16}{3}V$

2. $-\frac{16}{3}V$

3. $\frac{14}{3}V$

4. $-\frac{14}{3}V$

Q. Three charges $2q$, $-q$ and $-q$ are located at the vertices of an equilateral triangle. At the center of the triangle,

1. the field is non-zero but potential is zero
2. both field and potential are zero
3. the field is zero but potential is non-zero
4. both field and potential are non-zero

Q. In a region, the potential is represented by $V(x,y,z)=6x-8xy-8y+6yz$, where $V$ is in $\text{Volts}$ and $x,y,z$ are in $\text{meters}$. The electric force experienced by a charge of $2\text{coulombs}$ situated at the point $(1,1,1)$ is:-

1. $4\sqrt{35}\text{N}$
2. $30\text{N}$
3. $24\text{N}$
4. $6\sqrt{5}\text{N}$

Q. A uniform electric field pointing in positive x-direction exists in a region. Let A be the origin, B be the point on the x-axis at x = +1 cm and C be the point on the y-axis at y = +1 cm. Then the potentials at the points A, B and C satisfy

1. $V_A<V_B$
2. $V_A>V_B$
3. $V_A<V_C$
4. $V_A>V_C$

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

Q. If points A and B have a potential 3V and 5V respectively, and a dipole is brought between the two points, which way will its dipole moment align?
Given: Dipole is an arrangement of two equal and opposite charges separated by a very small fixed distance and Dipole moment is a vector quantity which points from negative to the positive charge of the dipole arrangement.

1. Towards A
2. Towards B
3. Neither A nor B
4. Can’t say

Q. A non-conducting sphere of radius $0.5\text{m}$ carries a total charge of $10\times {10}^{-10}\text{C}$ distributed uniformly which produces an electric field. Then the value of integral
$-\underset{\infty }{\overset{0}{\int }}\overrightarrow{E}\cdot \overrightarrow{dr}$ will be

1. $-9$
2. $27$
3. $0$
4. $-27$

Q. Potential in space is given by $V=X^2{Y}^2{Z}^2$
Find $\overrightarrow{E}$ at (1, -1, 2)

1. $-8\hat{i}+8\hat{j}-4\hat{k}$
   
2. $8\hat{i}-8\hat{j}-4\hat{k}$
   
3. $8\hat{i}+8\hat{j}+4\hat{k}$
   
4. $-8\hat{i}-8\hat{j}-4\hat{k}$

Q. The more the electric potential gradient between two points, the more will be the magnitude of electric field in between.

1. True
2. False

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