Potential Gradient and Relation between Electric Field and Potential

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. The electric field in a region surrounding the origin is uniform and along the x-axis. A small circle is drawn with the centre at the origin cutting the axes at points B, C, and D having co-ordinates (a, 0), (0, a), (– a, 0), (0, – a); respectively as shown in figure.Potential will be maximum at the point?

1. B
2. C
3. D

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. 20 N
4. 8 N

Q. The electric field in a region of space is given as $\overrightarrow{E}=(5x\hat{i}-2\hat{j})$. Potential at point $x=1,y=1$ is $V_1$ and potential at point (x = 2, y = 3)\) is $V_2$. Then $|V_1-V_2|=\frac{n}{2}$ . Find $n$ volts. (All quantities are in SI units)

Q. The electric potential V at any point O (x, y, z all in metres) in space is given by $V=4x^2$ volt. The electric field at the point (1m, 0, 2m) in volt/metre is

1. 8 along negative X- axis
2. 8 along positive X - axis
3. 16 along negative X - axis
4. 16 along positive Z - axis
   

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

1. None of these
2. 
3. 
4. 

Q. Electric field is directed towards

1. Either of them
2. Negative electric potential gradient
3. Nothing can be said
4. Positive electric potential gradient

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. 
2. 
3. 
4. 

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. 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. 
2. 
3. 
4.