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In this lesson, we will learn how to define the electric flux through a surface due to an electric field and find products of electric field and area vectors.

Q1:

Consider the uniform electric field N/C. What is its electric flux through a circular area of radius 2.0 m that lies in the -plane?

Q2:

A spherical rubber balloon carries a total charge 𝑄 = 6 . 0 0 µ C distributed uniformly over its surface. At 𝑡 = 0 . 0 0 s , the radius of the balloon is 𝑅 = 4 . 0 0 c m . The balloon is then slowly inflated until its radius reaches 2 𝑅 at 𝑡 = 4 . 0 0 s . Ignore any effect on the electric field due to the material of the balloon and assume that the radius increases uniformly with time.

Determine the electric field due to this charge at the surface of the balloon at 𝑡 = 1 6 . 0 s .

Determine the electric field due to this charge at the surface of radius 𝑅 at 𝑡 = 0 . 0 s .

Determine the electric field due to this charge at the surface of radius 2 𝑅 at 𝑡 = 4 . 0 0 s .

Q3:

Consider a uniform electric field modeled by the equation 𝐸 = ( 5 . 2 𝑗 + 3 . 5 𝑘 ) × 1 0 3 N/C. The field produces an electric flux through a circular area of radius 2.8 m.

How much flux is produced if the area lies in the 𝑦 𝑧 -plane?

How much flux is produced if the area is aligned at 3 0 ∘ above the 𝑥 𝑦 -plane?

Q4:

Two particles have equal magnitude charges of 𝑄 = 9 . 3 C, one charge is positive and the other negative. The particles are located on the 𝑥 -axis at points + 𝑎 and − 𝑎 , where 𝑎 = 5 . 5 cm, as shown in the diagram. What is the net electric flux due to these charges through a square surface of side 2 𝑎 that lies in the 𝑦 𝑧 -plane and is centered at the origin?

Q5:

Two large copper plates facing each other have charge densities ± 6 . 0 C/m^{2} on the surface facing the other plate and zero in between the plates. The electric flux through a 2.0 cm by 6.0 cm rectangular area between the plates varies with the orientation of the area.

Find the net electric flux through the area when it is parallel to the plates.

Find the net electric flux through the area when it is tilted to an angle 𝜃 = 3 6 ∘ from the direction parallel to the plates, as shown in the diagram.

Q6:

A cube whose sides are of length 𝑑 is placed in a uniform electric field of magnitude 𝐸 = 4 . 0 × 1 0 / 3 N C , and the field is perpendicular to two opposite faces of the cube. What is the net electric flux through the cube?

Q7:

A total charge of 5 . 6 × 1 0 − 6 C is distributed uniformly throughout a cubical volume whose sides are 12 cm long.

What is the charge density within the cube?

What is the electric flux through a cube that is concentric with the charge distribution and that has 12.0 cm long sides?

What is the electric flux through a cube that is concentric with the charge distribution and that has 15.0 cm long sides?

What is the electric flux through a spherical surface of radius 2.5 cm that is also concentric with the charge distribution?

Q8:

A square surface of area 2.0 cm^{2} is within a uniform electric field of magnitude 1 . 0 × 1 0 3 N/C. The amount of flux through the surface depends on how it is oriented relative to the direction of the electric field.

Find the electric flux through the surface when a line normal to the surface makes an angle of 3 0 ∘ with the electric field.

Find the electric flux through the surface when a line normal to the surface is perpendicular to the electric field.

Find the electric flux through the surface when a line normal to the surface is parallel to the electric field.

Q9:

An incandescent light bulb emits only 3.4 W of its power as visible light. What is the magnitude of the electric field of the emitted light at a distance of 7.0 m from the bulb?

Q10:

A uniform electric field of magnitude 2 . 3 × 1 0 4 N/C is perpendicular to a square sheet with sides 4.0 cm long. What is the electric flux through the sheet?

Q11:

A rectangular area with side lengths of 5.4 cm and 2.4 cm is between two parallel plates where there is a constant electric field of 35 N/C.

Find the electric flux parallel to the plates in this area.

Find the electric flux perpendicular to the plates in this area.

Find the electric flux normal to the area and making a 4 2 ∘ angle with the direction of the electric field.

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