A rectangle surface of sides 10cm and 15cm is placed inside a uniform ...
Solution:
Given,
Length of the rectangle surface, l = 15 cm = 0.15 m
Breadth of the rectangle surface, b = 10 cm = 0.1 m
Electric field, E = 25 V/m
Angle between the direction of electric field and the surface, θ = 30°
The flux of electric field through the rectangular surface can be calculated using the formula,
Φ = E A cosθ
where A is the area of the rectangular surface.
Area of the rectangular surface, A = l b
= 0.15 m × 0.1 m
= 0.015 m^2
Substituting the values in the formula, we get
Φ = 25 V/m × 0.015 m^2 × cos 30°
Φ = 0.1857 N/m^2C
Therefore, the correct option is B) 0.1857 N/m^2C.
Explanation:
The electric flux is a scalar quantity that represents the total number of electric field lines passing through a given area. It is proportional to the electric field strength and the area of the surface. In this problem, we are given the dimensions of the rectangular surface and the strength of the electric field. We can use the formula for electric flux to calculate the flux passing through the surface.
We know that the electric field lines are perpendicular to the surface at every point. However, in this problem, the surface is inclined at an angle of 30° with the direction of the electric field. Therefore, we need to take the component of the electric field that is perpendicular to the surface, which is given by E cosθ.
Finally, we multiply this component of the electric field with the area of the surface to get the electric flux passing through the surface.