An electric field 4.25 N/C produced by a given charged body makes an angle 60° to an area element 20 m^2. What is the electric flux due to the charge?*1 point35.0 Nm^2/C42.5 Nm^2/C43.75 Nm^2/C75.78 Nm^2/C
Question
An electric field 4.25 N/C produced by a given charged body makes an angle 60° to an area element 20 m^2. What is the electric flux due to the charge?*1 point35.0 Nm^2/C42.5 Nm^2/C43.75 Nm^2/C75.78 Nm^2/C
Solution 1
The electric flux (Φ) is given by the formula:
Φ = E * A * cos(θ)
where: E is the electric field = 4.25 N/C, A is the area = 20 m^2, and θ is the angle = 60°.
First, we need to convert the angle from degrees to radians because the trigonometric function in the formula uses radians.
1 radian = 180/π degrees So, 60 degrees = 60 * π/180 = π/3 radians
Now, we can substitute the values into the formula:
Φ = 4.25 N/C * 20 m^2 * cos(π/3) = 4.25 N/C * 20 m^2 * 0.5 (since cos(π/3) = 0.5) = 42.5 Nm^2/C
So, the electric flux due to the charge is 42.5 Nm^2/C.
Solution 2
The electric flux (Φ) is given by the formula:
Φ = E * A * cos(θ)
where: E is the electric field = 4.25 N/C, A is the area = 20 m^2, and θ is the angle = 60°.
First, we need to convert the angle from degrees to radians because the trigonometric function in the formula uses radians.
60 degrees = 60 * (π/180) = π/3 radians
Then, we substitute the values into the formula:
Φ = 4.25 N/C * 20 m^2 * cos(π/3) Φ = 85 Nm^2/C * 0.5 Φ = 42.5 Nm^2/C
So, the electric flux due to the charge is 42.5 Nm^2/C.
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