A flat disk 1.0 m in diameter is oriented so that the plane of the disk makes an angle of π/6 radians with a uniform electric field. If the field strength is 491.0 N/C, find the electric flux through the surface.
Please show step by step
What is E*area*cosAngle?
To find the electric flux through the surface of the flat disk, we can use the formula:
Electric flux (Φ) = Electric field strength (E) x Area (A) x cosine (θ),
where E is the electric field strength, A is the area of the surface, and θ is the angle between the electric field and the normal to the surface.
In this case, the electric field strength is given as 491.0 N/C, and the angle θ is π/6 radians.
Step 1: Calculate the area of the surface.
The surface area of a flat disk is given by the formula A = πr^2, where r is the radius of the disk.
In this problem, the diameter of the disk is given as 1.0 m, so the radius, r, is half of that, which is 0.5 m.
Now we can calculate the area:
A = π(0.5)^2 = π(0.25) = 0.7854 m^2
Step 2: Calculate the cosine of π/6 radians.
The cosine of π/6 radians is a known value. We can use a calculator or reference table to find the value of cos(π/6), which is √3/2.
Step 3: Plug the values into the formula and solve for electric flux.
Φ = E x A x cos(θ)
= 491.0 N/C x 0.7854 m^2 x √3/2
Now we can calculate the electric flux:
Φ ≈ 491.0 N/C x 0.7854 m^2 x (√3/2) = 272.65 N·m^2/C
Therefore, the electric flux through the surface of the flat disk is approximately 272.65 N·m^2/C.