Applied Physics (GSC-114) Week 5: The Electric Field

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Questions and Answers

What is the formula to calculate the magnitude of the electric field?

E = F/q

What are the units of electric field?

Newtons/Coulomb (N/C)

In which direction do electric field lines point for a positive charge?

Radially outwards

What principle states that the electric field due to many point charges is the vector sum of the fields due to individual charges?

Principle of superposition Signup and view all the answers

What is the electric field strength at a distance of 10 cm from a charge of 2 μC?

20 N/C Signup and view all the answers

What is the electric field at a point in the middle of two point charges of 4μC and −3.2μC separated by a distance of 4cm?

0 N/C Signup and view all the answers

What is a field in physics?

A field is something that has a value at every point in space. Signup and view all the answers

How is the electric field defined?

The electric field at a point in space is defined to be the amount of electric force per charge exerted at that point in space. Signup and view all the answers

Why does particle 1 'know' the presence of particle 2 in an electric field?

Particle 2 sets up an Electric Field in the space surrounding itself. Signup and view all the answers

How does the temperature field relate to the concept of a field in physics?

Temperature field represents the temperature at each point in space, similar to other fields in physics. Signup and view all the answers

What physical quantity does the electric field measure at a point in space?

Electric force per charge exerted at that point in space. Signup and view all the answers

What is the formula for surface charge density?

$ ext{Surface charge density} ( ext{σ}) = rac{ ext{charge}}{ ext{area}}$ Signup and view all the answers

What is the formula for linear charge density?

$ ext{Linear charge density} ( ext{λ}) = rac{ ext{charge}}{ ext{length}}$ Signup and view all the answers

How is the electric field of an extended object at a point calculated?

Calculate the electric field due to a charge element, replace charge element using charge density, sum the electric field components from all charge elements via integration. Signup and view all the answers

What is the formula for the electric field due to a uniformly charged thin rod near the rod?

$ ext{E}_{ ext{rod}} = rac{ ext{λx̂}}{2 ext{πε₀x}}$ Signup and view all the answers

What is the formula for the electric field due to a ring of charge distributed uniformly?

$ ext{E}_{ ext{ring}} = rac{ ext{QZ}}{4 ext{πε₀(Z² + R²)^(3/2)} ext{ẑ}$ Signup and view all the answers

What is the formula for the electric field due to a disk of charge distributed uniformly?

$ ext{E}_{ ext{disk}} = rac{ ext{σ}}{2 ext{ε₀}(1-Z)(Z² + R²)^(1/2)} ext{ẑ}$ Signup and view all the answers

Study Notes

Electric Field Basics

The magnitude of the electric field ( E ) is calculated using the formula ( E = \frac{F}{q} ), where ( F ) is the force experienced by a charge and ( q ) is the charge itself.
Electric field units are volts per meter (V/m) or newtons per coulomb (N/C).

Direction of Electric Field Lines

Electric field lines point away from positive charges and towards negative charges, indicating the direction a positive test charge would move in the field.

Principle of Superposition

The principle of superposition states that the electric field due to multiple point charges is the vector sum of the fields created by each charge individually.

Electric Field Strength Calculation

The electric field strength ( E ) at a distance of 10 cm from a charge of 2 μC can be calculated using ( E = \frac{k \cdot |Q|}{r^2} ), where ( k ) is Coulomb's constant, ( Q ) is the charge, and ( r ) is the distance. The value will depend on substituting known constants.

Electric Field Between Two Charges

To find the electric field at a point between two point charges (4 μC and -3.2 μC) separated by 4 cm, calculate individual fields due to each charge at that point and then vectorially add them considering their directions.

Concept of Field in Physics

A field in physics represents a region in which a physical quantity can be measured, with electric fields specifically representing regions exerting forces on charged particles.

Electric Field Definition

The electric field is defined as the force per unit charge experienced by a small positive test charge placed in the field.

Interaction of Particles

Particle 1 'knows' about particle 2 in an electric field due to the influence of force fields that propagate through space, affecting charges regardless of distance, instantaneously adjusting based on their relative positions.

Relation of Temperature Field to Physics

Temperature fields in physics describe variations in temperature across a region, reflecting a similar concept to other fields by showing how a quantity varies in space.

Measurement of Electric Field

The electric field measures the force exerted on a unit positive charge at a specific point in space.

Charge Density Formulas

Surface charge density ( \sigma ) is calculated using ( \sigma = \frac{Q}{A} ), where ( Q ) is the total charge and ( A ) is the area.
Linear charge density ( \lambda ) is calculated as ( \lambda = \frac{Q}{L} ), where ( L ) is the length along which the charge is distributed.

Electric Field Calculation for Extended Objects

The electric field of an extended object at a point in space is calculated by integrating contributions from infinitesimal charge elements over the entire object.

Electric Field Formulas for Charged Objects

The formula for the electric field due to a uniformly charged thin rod at a point near the rod is derived from integration taking into account charge distribution along the length.
For a uniformly charged ring, the electric field at a point along the axis of the ring is also calculated via integration of radial contributions from small charge elements.
For a uniformly charged disk, its electric field is derived using similar principles of superposition and integration over the disk’s surface.

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Description

Explore the concept of the electric field in applied physics, focusing on the value at every point in space. Learn how to determine the force on charged particles and understand the properties of electric fields.