A vertical wall (5.3 m multiplied by 2.3 m) in a house faces due east. A uniform electric field has a magnitude of 157 N/C. This field is parallel to the ground and points 38° north of east. What is the electric flux through the wall?
The E-field lines make an angle of 38 degrees with the normal to the wall. The flux is the E-field magnitude multiplied by wall area and cos 38.
E-Flux = 157*5.3*2.3*0.788
= 1508 N*m^2/C
Well, that's quite a shocking question! Let's calculate the electric flux through the wall using some electrifying humor.
Before we get to the math, remember that electric flux is a measure of the number of electric field lines passing through a surface. In this case, the surface is the vertical wall of the house.
To calculate the electric flux, we need to multiply the magnitude of the electric field by the area of the surface and the cosine of the angle between the electric field and the normal to the surface.
Now let's zing our way through the calculations!
Area of the wall = length x width
Area of the wall = 5.3 m x 2.3 m = 12.19 m²
Cosine of the angle between the electric field and the normal to the surface = cosine(38°)
Cosine of 38° ≈ 0.788
Electric flux = Electric field * Area * Cosine of the angle
Electric flux = 157 N/C * 12.19 m² * 0.788
Electric flux = 1500.71 N*m²/C
So the electric flux through the wall is approximately 1500.71 N*m²/C.
And there you have it! The electric flux is quite a jolt! Just remember to keep your humor charged and stay positively funny!
To find the electric flux through the wall, we can use the formula:
Flux = Electric field magnitude × Area × cos(θ)
where:
- Electric field magnitude is given as 157 N/C
- Area of the wall is given as the product of its dimensions: 5.3 m × 2.3 m
- θ is the angle between the electric field vector and the normal vector perpendicular to the wall's surface.
In this case, the electric field is parallel to the ground and points 38° north of east. Therefore, the angle between the electric field vector and the normal vector perpendicular to the wall's surface is 38°.
Plugging in the values:
Flux = 157 N/C × (5.3 m × 2.3 m) × cos(38°)
Calculating this expression will give you the value of the electric flux through the wall.
To find the electric flux through the wall, you need to multiply the magnitude of the electric field by the area of the wall and the angle between the electric field and the normal vector to the wall.
First, calculate the area of the wall by multiplying its length and height:
Area = 5.3 m x 2.3 m
Next, calculate the angle between the electric field and the normal vector to the wall. The problem states that the electric field points 38° north of east. Since the wall faces due east, the normal vector points directly outward from the wall, which is 90° counterclockwise from due east. Therefore, the angle between the electric field and the normal vector is 38° - 90° = -52° (negative sign indicates counterclockwise rotation).
Finally, calculate the electric flux through the wall by multiplying the magnitude of the electric field by the area of the wall and the cosine of the angle between them:
Electric Flux = Electric Field Magnitude x Area x cos(angle)
Substitute the given values into the equation to find the electric flux.