Now let’s use E=EAcos to calculate the electric flux through a disk with radius

Question

Now let’s use E=EAcos to calculate the electric flux through a disk with radius 0.10 m. The disk is oriented with its axis (the line through the center, perpendicular to the disk’s surface) at an angle of 30 to a uniform electric field E with magnitude 2.0×103N/C (Figure 1) . (a) What is the total electric flux through the disk? (b) What is the total flux through the disk if it is turned so that its plane is parallel to E ? (c) What is the total flux through the disk if it is turned so that its axis (marked by the dashed line perpendicular to the disk in the figure) is parallel to E ?

SOLUTION

SET UP AND SOLVE Part (a): The area is A=(0.10m)2=0.0314m2. From E=EAcos,

E==(2.0×103N/C)(0.0314m2)(cos30)54Nm2/C

Part (b): The axis of the disk is now perpendicular to E , so =90, cos=0, and E=0.

Part (c): The axis of the disk is parallel to E , so =0, cos=1, and, from E=EAcos,

E==(2.0×103N/C)(0.0314m2)(1)63Nm2/C

REFLECT The flux through the disk is greatest when its axis is parallel to E , and it is zero when E lies in the plane of the disk. That is, it is greatest when the most electric field lines pass through the disk, and it is zero when no lines pass through it.

Part A - Practice Problem:

What is the flux through the disk if its axis makes an angle of 80 with E ?

Explanation / Answer

A) total flux is E=EAcos,

so =80,
then   E = 2*10^3*0.0314*cos(80) = 10.9 N-m^2/C

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