Exam 23: Electric Fields

A +2.0-nC point charge is placed at one corner of a square (1.5 m on a side), and a −3.0-nC charge is placed on a corner diagonally away from the first charge. What is the magnitude of the electric field at either of the two unoccupied corners?

Imagine for a minute that the Moon is held in its orbit about the Earth by electrical forces rather than by gravitation. What electrical charges −Q on the Earth and +Q on the Moon are necessary to hold the Moon in a circular orbit with a period of 27.3 days? The Earth-Moon distance is 384 000 km and the mass of the Moon is 7.35 × 10²² kg.

The velocity of a particle (m = 10 mg, q = −4.0 μC) at t = 0 is 20 m/s in the positive x direction. If the particle moves in a uniform electric field of 20 N/C in the positive x direction, what is the particle's speed at t = 5.0 s?

A particle (q = 4.0 mC, m = 50 g) has a velocity of 25 m/s in the positive x direction when it first enters a region where the electric field is uniform (60 N/C in the positive y direction). What is the speed of the particle 5.0 s after it enters this region?

A particle (q = 3.0 mC, m = 20 g) has a speed of 20 m/s when it enters a region where the electric field has a constant magnitude of 80 N/C and a direction which is the same as the velocity of the particle. What is the speed of the particle 3.0 s after it enters this region?

A particle (mass = 5.0 g, charge = 40 mC) moves in a region of space where the electric field is uniform and is given by E_x = −5.5 N/C, E_y = E_z = 0. If the position and velocity of the particle at t = 0 are given by x = y = z = 0 and v_x = 50 m/s, v_y = v_z = 0, what is the distance from the origin to the particle at t = 2.0 s?

Three identical point charges Q are placed at the vertices of an equilateral triangle (length of each side = 2.0 m). If Q = 60 μC, what is the magnitude of the electrostatic force on any one of the charges?

Charge Q is uniformly distributed over a line segment of length 2L, as shown below. When the x-coordinate of point P is x, the magnitude of the y-component of the electric field at point P is

Suppose a uniform electric field of 4 N/C is in the positive x direction. When a charge is placed at and fixed to the origin, the resulting electric field on the x axis at x = 2 m becomes zero. What is the magnitude of the electric field at x = 4 m on the x axis at this time?

Three point charges, two positive and one negative, each having a magnitude of 20 μC are placed at the vertices of an equilateral triangle (30 cm on a side). What is the magnitude of the electrostatic force on the negative charge?

A charge of 50-μC is placed on the y axis at y = 3.0 cm and a 77-μC charge is placed on the x axis at x = 4.0 cm. If both charges are held fixed, what is the magnitude of the initial acceleration of an electron released from rest at the origin?

If a = 60 cm, b = 80 cm, Q = −6.0 nC, and q = 4.0 nC, what is the magnitude of the electric field at point P?

A particle (m = 50 g, q = 5.0 μC) is released from rest when it is 50 cm from a second particle (Q = −20 μC). Determine the magnitude of the initial acceleration of the 50-g particle.

A point charge Q is placed on the x axis at the origin. An identical point charge is placed on the x axis at x = −1.0 m and another at x = +1.0 m. If Q = 40 μC, what is the magnitude of the electrostatic force on the charge at x = +1.0 m?

If a = 3.0 mm, b = 4.0 mm, Q₁ = 60 nC, Q₂ = 80 nC, and q = 32 nC in the figure, what is the magnitude of the electric force on q?

If a = 60 cm, b = 80 cm, Q = −6.0 nC, and q = 3.0 nC in the figure, what is the magnitude of the electric field at point P?

A proton moving at 3 × 10⁴ m/s is projected at an angle of 30° above a horizontal plane. If an electric field of 400 N/C is directed downwards, how long does it take the proton to return to the horizontal plane? (HINT: Ignore gravity.) [m_Proton = 1.67 × 10−²⁷ kg, q_Proton = +1.6 × 10−¹⁹ C.]

Which one of the diagrams below is not a possible electric field configuration for a region of space which does not contain any charges?

Three 2.50 μC charges are placed on tiny conducting spheres at the ends of 1.00 m-long strings that are connected at 120° angles as shown below. The magnitude, in N, of the tension in any one of the strings is

Each of two small non-conducting spheres is charged positively, the combined charge being 40 μC. When the two spheres are 50 cm apart, each sphere is repelled from the other by a force of magnitude 2.0 N. Determine the magnitude of the smaller of the two charges.