Flashcards in Chapter 22 Deck (20):
A charged particle sets up an electric field (a vector quantity) in the surrounding space. If a second charged particle is located in that space, an electrostatic force acts on it due to the magnitude and direction of the field at its location.
The electric field E: at any point is defined in terms of the electrostatic force F: that would be exerted on a positive test charge q0 placed there:
E_vector = F_vector / q0
Electric field lines help us visualize the direction and magnitude of electric fields. The electric field vector at any point is tangent to the field line through that point. The density of field lines in that region is proportional to the magnitude of the electric field there. Thus, closer field lines represent a stronger field.
Electric field lines originate on positive charges and terminate on negative charges. So, a field line extending from a positive charge must end on a negative charge.
The magnitude of the electric field E_vector set up by a particle with charge q at distance r from the particle is
E = (1 / 4piE0) * (|q| / r^2)
The electric field vectors set up by a positively charged particle all point directly away from the particle. Those set up by a negatively charged particle all point directly toward the particle.
If more than one charged particle sets up an electric field at a point, the net electric field is the vector sum of the individual electric fields—electric fields obey the superposition principle.
An electric dipole consists of two particles with charges of equal magnitude q but opposite signs, separated by a small distance d.
The electric dipole moment p_vector has magnitude q*d and points from the negative charge to the positive charge.
The magnitude of the electric field set up by an electric dipole at a distant point on the dipole axis (which runs through both particles) can be written in terms of either the product q*d or the magnitude p of the dipole moment:
E = (1 / 2piE0) * (q*d / z^3) = (1 / 2piE0) * (p / z^3). where z is the distance between the point and the center of the dipole.
Because of the 1 / z^3 dependence, the field magnitude of an electric dipole decreases more rapidly with distance than the field magnitude of either of the individual charges forming the dipole, which depends on 1 / r^2.
The equation for the electric field set up by a particle does not apply to an extended object with charge (said to have a continuous charge distribution).
To find the electric field of an extended object at a point, we first consider the electric field set up by a charge element d*q in the object, where the element is small enough for us to apply the equation for a particle. Then we sum, via integration, components of the electric fields dE_vector from all the charge elements.
Because the individual electric fields dE_vector have different magnitudes and point in different directions, we first see if symmetry allows us to cancel out any of the components of the fields, to simplify the integration.
On the central axis through a uniformly charged disk,
E = (o- / 2E0)*(1 - (z / (z^2 + R^2)^1/2)), gives the electric field magnitude. Here z is the distance along the axis from the center of the disk, R is the radius of the disk, and o- is the surface charge density.
If a particle with charge q is placed in an external electric field E_vector, an electrostatic force F_vector acts on the particle:
F_vector = q*E_vector.
If charge q is positive, the force vector is in the same direction as the field vector. If charge q is negative, the force vector is in the opposite direction (the minus sign in the equation reverses the force vector from the field vector).
The torque on an electric dipole of dipole moment p_vector when placed in an external electric field E_vector is given by a cross product:
t_vector = p_vector X E_vector .
A potential energy U is associated with the orientation of
the dipole moment in the field, as given by a dot product:
U = -p_vector (dot prod.) E_vector