Chapter 16 Electric Field of Distributed Charges Question

Chapter 16 Electric Field of Distributed Charges

Question 1 (Chap. 16) A solid metal ball carrying negative excess charge is placed near a uniformly charged plastic ball. -Q +Q metal plastic Which one of the following statements is true? A. The electric field inside both balls is zero. B. The electric field inside the metal ball is zero, but it is nonzero inside the plastic ball. C. The electric fields inside both objects are nonzero and are pointing toward each other. D. The electric field inside the plastic ball is zero, but it is nonzero inside the metal ball.

Distributed Charges

General Procedure for Calculating Electric Field of Distributed Charges 1. Cut the charge distribution into pieces for which the field is known 2. Write an expression for the electric field due to one piece (i) Choose origin (ii) Write an expression for E and its components 3. Add up the contributions of all the pieces (i) Try to integrate symbolically (ii) If impossible – integrate numerically 4. Check the results: (i) Direction (ii) Units (iii) Special cases

A Uniformly Charged Thin Ring Origin: along the center of the ring Location of piece: described by q, where q = 0 is along the x axis. Step 1: Cut up the charge distribution into small pieces Step 2: Write E due to one piece

A Uniformly Charged Thin Ring Step 2: Write E due to one piece

A Uniformly Charged Thin Ring Step 2: Write E due to one piece Components x and y:

A Uniformly Charged Thin Ring Step 2: Write E due to one piece Component z:

A Uniformly Charged Thin Ring Step 3: Add up the contributions of all the pieces

A Uniformly Charged Thin Ring Step 4: Check the results Direction Units Special cases: Center of the ring (z=0): Ez=0 Far from the ring (z>>R):

A Uniformly Charged Thin Ring Distance dependence: Far from the ring (z>>R): Ez~1/z 2 Close to the ring (z<<R): Ez~z

A Uniformly Charged Thin Ring Electric field at other locations: needs numerical calculation

A Uniformly Charged Disk Section 15. 5 – home study!

Clicker Question is equal A B C D E

Uniformly Charged Disk Edge On Can a conducting disk have uniform charge distribution? A single metal disk cannot be uniformly charged: charges repel and concentrate at the edges

A Uniformly Charged Disk Along z axis Approximations: Close to the disk (0 < z < R) Very close to disk (0 < z << R) If z/R is extremely small

Field Far From the Disk Exact For z>>R Point Charge