A circular hoop of radius 0.60 m is immersed in a uniform electric field of 27.0 N/C. The electric field is at an angle of 30.0° to the plane of the hoop. Determine the electric flux through the hoop. (Enter the magnitude.)
N · m2/C
To determine the electric flux through the hoop, we can use the formula:
Electric flux = Electric field * Area * cos(theta)
First, let's find the area of the hoop. The formula for the area of a circle is:
Area = π * radius^2
Given that the radius of the hoop is 0.60 m:
Area = π * (0.60 m)^2
Next, we need to find the cosine of the angle theta. The given problem states that the angle between the electric field and the plane of the hoop is 30.0°.
cos(theta) = cos(30.0°)
Now we can calculate the electric flux. Given that the electric field is 27.0 N/C:
Electric flux = 27.0 N/C * π * (0.60 m)^2 * cos(30.0°)
Calculating this expression will give us the electric flux through the hoop.
determine the perpendicular area of the hoop: PI*r^2*cos60 (make certain this is the angle the E field is to the perpendicular to the loop plane).
Flux= E*areaPerpendicular