For the following electric field: E(x,y) = (x² + y²)î + 2xyŷ Calculate the potential in the xy plane. Assume the potential at the origin equals to zero, meaning (0,0) = 0. Select one: a. 4(x,y) = 3 -2xy2 ○ b. x(x, y) = - - xy c. y(x, y): == -x³-xy² ○ d. 2:3 (x, y): = - +xy² 3 e. (x, y) = x3 + xy² ○ f. (x, y): - 3 xy2 ×

(a) What is the potential between two points situated 10 cm and 20 cm from a 3.0C point charge? (b) To what location should the point at 20 cm be moved to increase this potential difference by a factor of two?

A very large sheet of insulating material has had an excess of electrons placed on it to a surface charge density of 3.00nC/m2 . (a) As the distance from the sheet increases, does the potential increase or decrease? Can you explain why without any calculations? Does the location of your reference point matter? (b) What is the shape of the equipotential surfaces? (c) What is the spacing between surfaces that differ by 1.00 V?

An electron moving parallel to the x axis has an initial speed of 3.70 106 m/s at the origin. Its speed is reduced to 1.40 105 m/s at the point x = 2.00 cm. (a) Calculate the electric potential difference between the origin and that point. (b) Which point is at the higher potential?

Some cell walls in the human body have a layer of negative charge on the inside surface. Suppose that the surface charge densities are 0.50103C/m2 the cell wall is 5.0109m thick, and the cell wall material has a dielectric constant of = 5.4. (a) Find the magnitude of the electric field in the wall between two charge layers, (b) Find the potential difference between the inside and the outside of the cell. Which is at higher potential? (c) A typical cell in die human body has volume 1016m3 . Estimate the total electrical field energy stored in the wall of a cell of this size when assuming that the cell is spherical. (Hint: Calculate the volume of the cell wall.)

A spherical capacitor is formed from two concentric spherical conducting spheres separated by vacuum. Tire inner sphere has radius 12.5 cm and the outer sphere has radius 14.8 cm. A potential difference of 120 V is applied to the capacitor, (a) What is the capacitance of the capacitor? tb) What is the magnitude of the electrical field at r = 12.6 cm, just outside the inner sphere? (c) What is the magnitude of the electrical field at r = 14.7 cm, just inside the outer sphere? (d) For a parallel-plate capacitor the electrical field is uniform in the region between the plates, except near the edges of the plates. Is this also true for a spherical capacitor?

The surface charge density on a long straight metallic pipe is . What is the electric potential outside and inside the pipe? Assume the pipe has a diameter of 2a.

(a) A sphere has a surface uniformly charged with 1.00 C. At what distance from its center is the potential 5.00 MV? (b) What does your answer imply about the practical aspect of isolating such a large charge?

A rod of length L (Fig. P24.25) lies along the x axis with its left end at the origin. It has a nonuniform charge density = x, where is a positive constant. (a) What are the units of ? (b) Calculate the electric potential at A. Figure P24.25 Problems 25 and 26.

(a) What is the capacitance of a parallel plate capacitor having plates of area 1.50 m2 that are separated by 0.0200 mm of neoprene rubber? (b) What charge does it hold when 9.00 V is applied to it?