Try it on paper first. A hint, the key idea and the worked solution are here when you need them.
A rectangular frame m long and m wide is placed in a uniform electric field of N/C. The field makes an angle of with the plane of the frame. Find the angle between the field and the normal to the frame, the flux through the frame, and the largest flux that the frame could have in this field.
The flux through a flat surface in a uniform field is , with the angle between the field and the normal to the surface. For a closed surface the normal points outward: lines that leave count as positive and lines that enter as negative. In a uniform field the net flux through a closed surface is zero.
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Given. N/C, , and the field makes with the plane.
Step 1. The angle with the normal. .
Step 2. The flux. .
Step 3. The largest flux. It happens when the frame faces the field. .
Answer: , and .
Check. The flux with the plane angle is . It is the same, as it should be.
Watch out. Putting straight into the cosine would give . That is wrong, because the cosine needs the angle with the normal.
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