An electrostatic field is given by
Determine the work done in moving the charge
(a) from (0,0,0) to (4,0,0) m
(b) from (4,0,0) to (4,2,0) m
(c) from (4,2,0) to (0,0,0) m along a straight path.
Two plastic spheres, each carrying charge uniformly distributed throughout its interior, are initially placed in contact and then released. The first sphere has a diameter of 60 cm, a mass of 50 g, and contains of charge. The second sphere has a diameter of 40 cm, a mass of 150 g and contains of charge. Assume that no other forces are acting on them.
(a) Find the maximum speed achieved by the first sphere.
(b) Find the maximum acceleration achieved by the first sphere.
A particle with a charge of +8 nC is in a uniform electric field E directed to the left. It is released from rest and moves to the left. After it has moved 3 cm, its kinetic energy is found to be
(a) What work was done by the electric force?
(b) What is the potential of the starting point with respect to the endpoint?
(c) What is the magnitude of E?
A total electric charge of 8 nC is distributed uniformly over the surface of a metal sphere with a radius of 27 cm. If the potential is zero at a point at infinity, find the value of the potential at the following distances from the center of the sphere.
(a) 52 cm
(b) 20 cm
(c) 9 cm
A potential difference of 10 kV is established between parallel plates in air.
(a) If the air becomes electrically conducting when the electric field exceeds , what is the minimum separation of the plates?
(b) When the separation has the minimum value calculated in part (a), what is the surface charge density on each plate?
An alpha particle with kinetic energy 10 MeV makes a head-on collision with a lead nucleus at rest. What is the distance of closest approach of the two particles? (Assume that the lead nucleus remains stationary and that it may be treated as a point charge. The atomic number of lead is 82. The alpha particle is a helium nucleus, with atomic number 2.)
In a certain region of space, the electric potential is is , , where A, B, and C are positive constants.
(a) Calculate the x-, y-, and z-components of the electric field.
(b) At which points is the electric field equal to zero?
A point charge is held stationary at the origin. A second point charge is moves from the point x = 0.20 m, y = 0 to the point x = 0.3 m, y = 0.35 m. How much work is done by the electric force on ?
A parallel-plate air capacitor of capacitance of 100 pF has a charge of magnitude 0.1 µC on each plate. The plates are 0.5 mm apart.
(a) What is the potential difference between the plates?
(b) What is the area of each plate?
(c) What is the electric-field magnitude between the plates?
(d) What is the surface charge density on each plate?
A particle of charge Q and mass m is accelerated from rest through a potential difference V, attaining a kinetic energy K. What is the kinetic energy of a particle of charge 2Q and mass m/2 that is accelerated from rest through the same potential difference?
Initially, sphere A has a charge of -50e and a sphere B has a charge of +20e. The spheres are made of conducting material and are identical in size. If the spheres then touch, what is the resulting charge on sphere A?
A 240 Volts circuit used energy when left running for 30 minutes. How much electric charge (in Coulombs) flowed in the 30 minutes?
How much work is done in moving a charge of 2 coulombs from a point at 118 volts to a point at 128 volts?
How much energy is given to a charge of 20 nC passing through a 6 V battery?
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