Q: Which of the following best describes the relationship between electric potential $$V(\vec{r})$$ and electric field $$\vec{E}(\vec{r})$$?

$$\vec{E}(\vec{r}) = -\vec{\nabla} V(\vec{r})$$

Question 1

Which of the following best describes the relationship between electric potential $$V(\vec{r})$$ and electric field $$\vec{E}(\vec{r})$$?

Accepted Answer

$$\vec{E}(\vec{r}) = -\vec{
abla} V(\vec{r})$$

Question 2

A test charge $$q$$ moves from point A to point B in a non-uniform electric field $$\vec{E}(\vec{r}). $$Which expression gives the work done by the field?

Accepted Answer

$$W_{A \rightarrow B} = q \int_A^B d\vec{r} \cdot \vec{E}(\vec{r})$$

Question 3

What is the electric potential $$V(\vec{r}) at a $$distance $$r$$ from a point charge $$Q$$ located at the origin?

Accepted Answer

$$V(\vec{r}) = k_e \frac{Q}{r}$$

Question 4

If the electric potential changes as $$V(x, y, z) = E_0$ x e$$^{-(r/a)^2}$$, where r$$ = \sqrt{$$x^2$$ + $$y^2$$ + $$z^2$$}$$, what is the x$-component of the electric field E_x$?

Accepted Answer

$$E_x = -E_0$ e$$^{-(r/a)^2}$$ + \frac{2E_0 x^2$}{a^2$} e$$^{-(r/a)^2}$$

Question 5

Which statement about equipotential surfaces is correct?

Accepted Answer

Electric field lines are perpendicular to equipotential surfaces.

Question 6

An Argon ion ($$m = 40 a.m.u$$., $$1 a.m.u$$. $$= 1.66 	imes 10$$^{-27}$$ kg) is accelerated from rest by a uniform electric field of 10$ kV/m between two grids separated by d = 10$ cm. What is its velocity when it leaves the acceleration region?

Accepted Answer

$$v = \sqrt{\frac{2qEd}{m}}$$

Question 7

What is the unit of electric potential?

Accepted Answer

Volt (V)

Question 8

If two point charges $$q_1 = -1$$ \mu$$C and q_2$ = -2 \muC $$are released from rest at a distance $$d = 10 cm$$, what is the direction of their motion?

Accepted Answer

They move away from each other.

Question 9

Which of the following is true about the work done by the electric field when moving a charge between two points?

Accepted Answer

It is independent of the path taken between the points.

Question 10

What is the energy change (in joules) of an elementary charge $$e$$ undergoing a potential difference of $$1 V$$?

Accepted Answer

$$1.602 	imes 10$$^{-19}$$ J

Question 11

For a charge distribution, which expression gives the electric potential $$V(\vec{r}) at a $$point $$\vec{r}$$?

Accepted Answer

$$V(\vec{r}) = k_e \int \frac{dQ(\vec{r}')}{|\vec{r} - \vec{r}'|}$$

Question 12

If the density of equipotential surfaces increases in a particular direction, what can be inferred about the electric field in that region?

Accepted Answer

The electric field is stronger where the surfaces are denser.

Question 13

Which mathematical operator is used to express the gradient of electric potential?

Accepted Answer

$$\vec{
abla}$$

Question 14

A charge $$q is $$moved by $$\Delta \vec{r} in an $$electric field $$\vec{E}. $$What is the change in electric potential $$\Delta V$$?

Accepted Answer

$$\Delta V = -\vec{E} \cdot \Delta \vec{r}$$

Question 15

Which of the following is a correct expression for the $$x-$$component of the electric field in terms of electric potential?

Accepted Answer

$$E_x = -\frac{\partial V}{\partial x}$$

Question 16

If a charge $$q is $$moved from $$\vec{r}_0 to$$ $$\vec{r}$$, what is the potential energy at $$\vec{r}$$?

Accepted Answer

$$U(\vec{r}) = -q \$$int_{\vec{r}$$_0}^{\vec{r}} d\vec{r}' \cdot \vec{E}(\vec{r}') + U(\vec{r}_0)$$

Question 17

Which of the following best describes the equipotential surfaces for a point charge located at the origin?

Accepted Answer

Concentric spheres

Question 18

If the electric field is uniform and points in the $$x-$$direction, what is the electric potential difference between two points separated by $$\Delta x$$?

Accepted Answer

$$\Delta V = -E_x \Delta x$$

Question 19

Which of the following is NOT a correct unit for electric field?

Accepted Answer

J/C

Electric Potential and Potential Energy in Electrostatics

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