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Q. 14

Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
Found in: Page 653

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Short Answer

Twodiameter charged rings face each other,apart. The left ring is charged toand the right ring is charged to.

a. What is the electric field, both magnitude and direction, at the midpoint between the two rings?

b. What is the force on a proton at the midpoint?

a.The electric field for both magnitude and direction, at the midpoint between the two rings is.

b.The force on a proton at the midpoint is.

See the step by step solution

Step by Step Solution

Step 1: Figure for model of given situation

First, we have to draw a model of the given situation.

Every charge point on one ring has an equal and opposite charge point on the other ring, thereby doubling the charge size.

We can find the magnitude of the electric field on the point by doubling the electric field exerted on the midpoint by either of the discs.

Step 2: Calculation of x (part a)

a. To find the value of

Distance to the midpoint from the centers of the rings,by dividing the distance between the centers of the rings by .

Step 3: Calculation of electric field (part a)

Electric field formula is,

Because , and are all constants,

When integrating the formula to get, we can remove anything involving those variables from the integral.

This leaves us with only inside of the integral, which just transforms into.

Step 4: Calculation of force (part b)

b) The formula is as follows:

, to determine the force exerted by the electric field.

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