What is the electric field strength

Question

Two 10-cm-diameter charged rings face each other, 25.0 cmcm apart. Both rings are charged to + 40.0 nCnC . What is the electric field strength

at the midpoint between the two rings?

at the center of the left ring?

Answer 1

Step 1:

Diameter of the ring is .

Charge on each ring is .

Distance between the rings is  m.

Radius of the ring is  m.

Electric field strength for a ring with radius  and distance  from the center of the ring is .

Find the electric field strength mid point.

Charge on mid point is resultant of both left and right rings on that point.

Electric field strength Contribution of left ring:

Distance from the left ring t the mid point is  m.

Substitute corresponding values in the formula.

.

Since mid point is considered , the magnitude of the right ring contribution is also same as the left ring and is in opposite direction.

.

Step 2:

(ii)

Find the field strength at the center of the left ring.

Contribution of left ring:

Distance from the left ring to that point itself is zero.

Contribution of right ring:

Distance from the right ring to center of the left ring is  m.

Substitute corresponding values in the formula.

.

Therefore field strength at the center of the left ring is .

Solution:

(i) Electric field strength mid point is .

(ii) Electric field strength at the center of the left ring is .