The electric flux through the surface shown in Figure Ex27.10 is 15.0 Nm2/C, and the electric field makes an angle α = 70° with the surface. What is the electric field strength? The surface is a 10cm by 10cm square.
To find the electric field strength, we can use the formula:
Electric flux = Electric field strength × Area × cos(α)
Given information:
Electric flux (Φ) = 15.0 Nm²/C
Angle (α) = 70°
Surface area = 10 cm × 10 cm
First, we need to convert the surface area from square centimeters to square meters. Since 1 meter = 100 centimeters, the surface area is:
Surface area = (10 cm × 10 cm) / (100 cm/m) = 1 m²
Now we can rearrange the formula:
Electric field strength = Electric flux / (Area × cos(α))
Substituting the given values, we have:
Electric field strength = 15.0 Nm²/C / (1 m² × cos(70°))
To calculate cos(70°), we need to convert the angle to radians, because calculator functions typically use radians. The conversion is:
70° × (π/180) = 1.22173 radians
Now we substitute the values into the equation:
Electric field strength = 15.0 Nm²/C / (1 m² × cos(1.22173 radians))
Using a calculator or a computer program, we can evaluate the cos(1.22173 radians) = 0.39578
Electric field strength = 15.0 Nm²/C / (1 m² × 0.39578)
Simplifying:
Electric field strength ≈ 37.89 N/C
Therefore, the electric field strength is approximately 37.89 N/C.