7. Electric Fields A.md

type

status

date

slug

summary

category

icon

password

Section 18.1: Electric fields and field lines

Definition Dictation: Define an electric field and describe it as a field of force. Answer: An electric field is a region around a charged particle where a force would be exerted on other charged particles. It is defined as the force per unit positive charge.

Formula Dictation and Application: Recall the formula that relates the force on a charge in an electric field and use it to calculate the force on a charge of C in an electric field with a strength of . Answer: The formula is , where is the force in newtons, is the charge in coulombs, and is the electric field strength in newtons per coulomb. For the given values, .

Representation: How are electric field lines used to represent an electric field, and what rules must be followed in their representation? Answer: Electric field lines are used to represent the direction and relative strength of an electric field. The lines point away from positive charges and toward negative charges, indicating the direction of the force on a positive test charge. The density of the lines represents the strength of the field: closer lines mean a stronger field. The lines must start on positive charges and end on negative charges, or at infinity, and never cross each other.

Section 18.2: Uniform electric fields

Formula Dictation and Application: Recall the formula that relates the electric field strength to the potential difference and separation between charged parallel plates and use it to find the field strength if the potential difference is and the plate separation is . Answer: The formula is , where is the electric field strength, is the potential difference, and is the separation between the plates. Using the given values, .

Effect on Charged Particles: Describe the motion of a positively charged particle when it enters a uniform electric field perpendicular to the field lines, and provide the formula used to calculate the force on the particle. Answer: When a positively charged particle enters a uniform electric field perpendicular to the field lines, it experiences a constant force in the direction of the field. This force causes the particle to accelerate in the direction of the electric field, resulting in a parabolic path if the particle had an initial velocity perpendicular to the field. The formula used to calculate the force on the particle is , where is the force, is the charge of the particle, and is the electric field strength.

Section 18.3: Electric force between point charges

Conceptual Understanding: Explain why, for a point outside a spherical conductor, the charge on the sphere may be considered to be at its centre. Answer: For a point outside a spherical conductor, the electric field is identical to that which would be produced if the same amount of charge were concentrated at a point at the centre of the sphere. This is due to the symmetry of a sphere, where all parts of the charge distribution contribute to the electric field in such a way that the resulting field is radial and depends only on the total charge and the distance from the centre, as if the charge were a point charge at the centre.

Formula Dictation and Application: Recall Coulomb's law and use it to calculate the force between two point charges of C and C separated by a distance of m in free space. (Assume the value of to be C²/Nm² for calculation simplicity.) Answer: Coulomb's law is given by . Substituting the given values, we get .

Section 18.4: Electric field of a point charge

Formula Dictation and Application: Recall the formula for the electric field strength due to a point charge and calculate the field strength at a distance of m from a point charge of C. Answer: The formula for the electric field strength due to a point charge is . Using the given values, .

Section 18.5: Electric potential

Definition Dictation: Define electric potential at a point. Answer: Electric potential at a point is defined as the work done per unit positive charge in bringing a small test charge from infinity to that point.

Conceptual Understanding: Explain why the electric field at a point is equal to the negative of the potential gradient at that point. Answer: The electric field at a point is the force per unit charge experienced by a positive test charge placed at that point. The potential gradient is the rate at which the electric potential changes with distance. The electric field is directed from regions of higher potential to lower potential, hence it is equal to the negative of the potential gradient, indicating that the force on a positive charge is in the direction of decreasing potential.

Formula Dictation and Application: Use the formula for the electric potential in the field due to a point charge to calculate the potential at a distance of m from a point charge of C. Answer: The formula for the electric potential due to a point charge is . Substituting the given values, .

Application of Electric Potential Energy: Calculate the electric potential energy of two point charges of C and C separated by a distance of m. Answer: The formula for the electric potential energy (EP) between two point charges is . Using the given values, .