There is a rectangle of length 1.40 cm and width 6.10 cm in the xy-plane. If the electric field can be expressed by (100.[^(i)] +234 [^(k)]) N/C, what is the flux through the rectangle?
hey - only the component in the k direction passes through your loop :)
flux=E dot area, and the only dot
flux=(100i+234k).(area k)
so flux=234*area
To find the flux through the rectangle, we need to calculate the electric field passing through it and then multiply it by the area of the rectangle.
First, let's calculate the area of the rectangle. The formula for the area of a rectangle is given by:
Area = length * width
In this case, the length is 1.40 cm and the width is 6.10 cm, so the area is:
Area = 1.40 cm * 6.10 cm = 8.54 cm²
Now let's calculate the electric field passing through the rectangle.
The electric field is given by (100.[^(i)] + 234[^(k)]) N/C. This indicates that the electric field has components in the x and z directions, and no component in the y direction.
To find the electric field passing through the rectangle, we need to consider the z-component only, since the rectangle lies in the xy-plane.
So, the z-component of the electric field is 234 N/C.
Finally, we can find the flux through the rectangle by multiplying the electric field by the area of the rectangle:
Flux = Electric field * Area
Flux = 234 N/C * 8.54 cm²
Note: It is important to convert the area to square meters, as the SI unit for electric field is N/C and the unit of area should be in square meters.
To convert cm² to square meters, we divide the area by 10,000:
Flux = 234 N/C * (8.54 cm² / 10,000)
Flux = 1.9956 N·m²/C
Therefore, the flux through the rectangle is 1.9956 N·m²/C.