24. Electric Force & Field; Gauss' Law

A proton is released in a uniform electric field, and it experiences an electric force of 1.68 x 10^-14 N toward the south. Find the magnitude and direction of the electric field.

Determine the magnitude of the acceleration experienced by an electron in an electric field of 756 N/C. How does the direction of the acceleration depend on the direction of the field at that point?

What is the electric field strength at a point in space where a proton experiences an acceleration of 2.4 million “g’s”?

Calculate the electric field at the center of a square 42.5 cm on a side if one corner is occupied by a -33.8 μC charge and the other three are occupied by -22.0 μC charges.

At what position, 𝓍 = 𝓍_m, is the magnitude of the electric field along the axis of the ring of Example 21–10 a maximum?

Estimate the electric field at a point 2.40 cm perpendicular to the midpoint of a uniformly charged 2.00-m-long thin wire carrying a total charge of 7.45 μC.

Consider an oil droplet of mass m and charge q. We want to determine the charge on the droplet in a Millikan-type experiment. We will do this in several steps. Assume, for simplicity, that the charge is positive and that the electric field between the plates points upward. An electric field is established by applying a potential difference to the plates. It is found that a field of strength E₀ will cause the droplet to be suspended motionless. Write an expression for the droplet's charge in terms of the suspending field E₀ and the droplet's weight mg.

Consider an oil droplet of mass m and charge q. We want to determine the charge on the droplet in a Millikan-type experiment. We will do this in several steps. Assume, for simplicity, that the charge is positive and that the electric field between the plates points upward. A spherical object of radius r moving slowly through the air is known to experience a retarding force F_drag = −6πηrv where η is the viscosity of the air. Use this and your answer to part b to show that a spherical droplet of density ρ falling with a terminal velocity v_term has a radius. $r=\sqrt{\frac{9\eta v_{term}}{2\rho g}}$

The identical small spheres shown in FIGURE P22.64 are charged to +100 nC and −100 nC. They hang as shown in a 100,000 N/C electric field. What is the mass of each sphere?

An electret is similar to a magnet, but rather than being permanently magnetized, it has a permanent electric dipole moment. Suppose a small electret with electric dipole moment 1.0×10⁻⁷ C m is 25 cm from a small ball charged to +25 nC, with the ball on the axis of the electric dipole. What is the magnitude of the electric force on the ball?

A point charge $q_1=-4.00$ nC is at the point $x=0.600$ m, $y=0.800$ m, and a second point charge $q_2=+6.00$ nC is at the point $x=0.600$ m, $y=0$. Calculate the magnitude and direction of the net electric field at the origin due to these two point charges.

A $-4.00$-nC point charge is at the origin, and a second $-5.00$-nC point charge is on the $x$-axis at $x=0.800$ m. Find the electric field (magnitude and direction) at each of the following points on the $x$-axis: (i) $x=0.200$ m; (ii) $x=1.20$ m; (iii) $x=-0.200$ m.

Calculate the magnitude and direction (relative to the $+x$-axis) of the electric field in Example $21.6$. Example $21.6$: A point charge $q=-8.0$ nC is located at the origin. Find the electric-field vector at the field point $x=1.2$ m, $y=-1.6$ m.

The earth has a net electric charge that causes a field at points near its surface equal to $150$ $N/C$ and directed in toward the center of the earth. What magnitude and sign of charge would a $60$-kg human have to acquire to overcome his or her weight by the force exerted by the earth's electric field?

The earth has a net electric charge that causes a field at points near its surface equal to $150$ $N/C$ and directed in toward the center of the earth. What would be the force of repulsion between two people each with the charge calculated in part (a) and separated by a distance of $100$ m? Is use of the earth's electric field a feasible means of flight? Why or why not? Note: Part (a) asked for what magnitude and sign of charge would a $60$-kg human have to acquire to overcome his or her weight by the force exerted by the earth's electric field.