A circular surface with a radius of 0.058 m is exposed to a uniform external electric field of magnitude 1.49 104 N/C. The electric flux through the surface is 74 N · m2/C. What is the angle between the direction of the electric field and the normal to the surface?
To find the angle between the direction of the electric field and the normal to the surface, we can use the formula:
Electric Flux = Electric Field * Surface Area * cos(theta)
Where:
Electric Flux is given as 74 N·m²/C
Electric Field is given as 1.49 * 10^4 N/C
Surface Area of the circular surface can be calculated using the formula A = π * r², where r is the radius given as 0.058 m.
Let's calculate the Surface Area first:
A = π * r²
A = π * (0.058 m)²
A ≈ 0.0106 m²
Now we can rearrange the formula to solve for theta:
cos(theta) = Electric Flux / (Electric Field * Surface Area)
cos(theta) = 74 N·m²/C / (1.49 * 10^4 N/C * 0.0106 m²)
cos(theta) ≈ 4.4644
To find the angle theta, we can take the inverse cosine (cos⁻¹) of 4.4644:
theta ≈ cos⁻¹(4.4644)
The angle theta represents the angle between the direction of the electric field and the normal to the surface.