Electric Potential in a Uniform Electric Field Quiz

PDF page 901: In the previous section, we explored the relationship between voltage and energy. In this section, we will explore the relationship between voltage and electric field. For example, a uniform electric field is produced by placing a potential difference (or voltage) across two parallel metal plates, labeled A and B. (See Figure 19.5.) Examining this will tell us what voltage is needed to produce a certain electric field strength; it will also reveal a more fundamental relationship between electric potential and electric field. From a physicist’s point of view, either or can be used to describe any charge distribution. is most closely tied to energy, whereas is most closely related to force. is a scalar quantity and has no direction, while is a vector quantity, having both magnitude and direction. (Note that the magnitude of the electric field strength, a scalar quantity, is represented by below.) The relationship between and is revealed by calculating the work done by the force in moving a charge from point A to point B. But, as noted in Electric Potential Energy: Potential Difference, this is complex for arbitrary charge distributions, requiring calculus. We therefore look at a uniform electric field as an interesting special case.

PDF page 901: In the previous section, we explored the relationship between voltage and energy. In this section, we will explore the relationship between voltage and electric field. For example, a uniform electric field is produced by placing a potential difference (or voltage) across two parallel metal plates, labeled A and B. (See Figure 19.5.) Examining this will tell us what voltage is needed to produce a certain electric field strength; it will also reveal a more fundamental relationship between electric potential and electric field. From a physicist’s point of view, either or can be used to describe any charge distribution. is most closely tied to energy, whereas is most closely related to force. is a scalar quantity and has no direction, while is a vector quantity, having both magnitude and direction. (Note that the magnitude of the electric field strength, a scalar quantity, is represented by below.) The relationship between and is revealed by calculating the work done by the force in moving a charge from point A to point B. But, as noted in Electric Potential Energy: Potential Difference, this is complex for arbitrary charge distributions, requiring calculus. We therefore look at a uniform electric field as an interesting special case.

PDF page 901: In the previous section, we explored the relationship between voltage and energy. In this section, we will explore the relationship between voltage and electric field. For example, a uniform electric field is produced by placing a potential difference (or voltage) across two parallel metal plates, labeled A and B. (See Figure 19.5.) Examining this will tell us what voltage is needed to produce a certain electric field strength; it will also reveal a more fundamental relationship between electric potential and electric field. From a physicist’s point of view, either or can be used to describe any charge distribution. is most closely tied to energy, whereas is most closely related to force. is a scalar quantity and has no direction, while is a vector quantity, having both magnitude and direction. (Note that the magnitude of the electric field strength, a scalar quantity, is represented by below.) The relationship between and is revealed by calculating the work done by the force in moving a charge from point A to point B. But, as noted in Electric Potential Energy: Potential Difference, this is complex for arbitrary charge distributions, requiring calculus. We therefore look at a uniform electric field as an interesting special case.

PDF page 901: In the previous section, we explored the relationship between voltage and energy. In this section, we will explore the relationship between voltage and electric field. For example, a uniform electric field is produced by placing a potential difference (or voltage) across two parallel metal plates, labeled A and B. (See Figure 19.5.) Examining this will tell us what voltage is needed to produce a certain electric field strength; it will also reveal a more fundamental relationship between electric potential and electric field. From a physicist’s point of view, either or can be used to describe any charge distribution. is most closely tied to energy, whereas is most closely related to force. is a scalar quantity and has no direction, while is a vector quantity, having both magnitude and direction. (Note that the magnitude of the electric field strength, a scalar quantity, is represented by below.) The relationship between and is revealed by calculating the work done by the force in moving a charge from point A to point B. But, as noted in Electric Potential Energy: Potential Difference, this is complex for arbitrary charge distributions, requiring calculus. We therefore look at a uniform electric field as an interesting special case.

PDF page 903: or 19.30 (The answer is quoted to only two digits, since the maximum field strength is approximate.) Discussion One of the implications of this result is that it takes about 75 kV to make a spark jump across a 2.5 cm (1 in.) gap, or 150 kV for a 5 cm spark. This limits the voltages that can exist between conductors, perhaps on a power transmission line. A smaller voltage will cause a spark if there are points on the surface, since points create greater fields than smooth surfaces. Humid air breaks down at a lower field strength, meaning that a smaller voltage will make a spark jump through humid air. The largest voltages can be built up, say with static electricity, on dry days.

PDF page 903: or 19.30 (The answer is quoted to only two digits, since the maximum field strength is approximate.) Discussion One of the implications of this result is that it takes about 75 kV to make a spark jump across a 2.5 cm (1 in.) gap, or 150 kV for a 5 cm spark. This limits the voltages that can exist between conductors, perhaps on a power transmission line. A smaller voltage will cause a spark if there are points on the surface, since points create greater fields than smooth surfaces. Humid air breaks down at a lower field strength, meaning that a smaller voltage will make a spark jump through humid air. The largest voltages can be built up, say with static electricity, on dry days.

PDF page 904: (a) An electron gun has parallel plates separated by 4.00 cm and gives electrons 25.0 keV of energy. What is the

PDF page 904: Since the electron is a single charge and is given 25.0 keV of energy, the potential difference must be 25.0 kV. Entering this value for and the plate separation of 0.0400 m, we obtain

PDF page 904: In more general situations, regardless of whether the electric field is uniform, it points in the direction of decreasing potential, because the force on a positive charge is in the direction of and also in the direction of lower potential

PDF page 904: . Furthermore, the magnitude of equals the rate of decrease of with distance. The faster decreases over

PDF page 904: distance, the greater the electric field. In equation form, the general relationship between voltage and electric field is

PDF page 904: where is the distance over which the change in potential, , takes place. The minus sign tells us that points in the direction of decreasing potential. The electric field is said to be the gradient (as in grade or slope) of the electric potential.

PDF page 905: where is the distance over which the change in potential, , takes place. The minus sign tells us that points in the direction of decreasing potential. The electric field is said to be the gradient (as in grade or slope) of the electric potential.

PDF page 901: In the previous section, we explored the relationship between voltage and energy. In this section, we will explore the relationship between voltage and electric field. For example, a uniform electric field is produced by placing a potential difference (or voltage) across two parallel metal plates, labeled A and B. (See Figure 19.5.) Examining this will tell us what voltage is needed to produce a certain electric field strength; it will also reveal a more fundamental relationship between electric potential and electric field. From a physicist’s point of view, either or can be used to describe any charge distribution. is most closely tied to energy, whereas is most closely related to force. is a scalar quantity and has no direction, while is a vector quantity, having both magnitude and direction. (Note that the magnitude of the electric field strength, a scalar quantity, is represented by below.) The relationship between and is revealed by calculating the work done by the force in moving a charge from point A to point B. But, as noted in Electric Potential Energy: Potential Difference, this is complex for arbitrary charge distributions, requiring calculus. We therefore look at a uniform electric field as an interesting special case.