Explanation Electric field is defined as electric force per unit charge. The direction of electric field is proceeding in the direction of force. The unit of electric field is Newton per Coulomb (N/C) or Volts/meter (V/m). The electric field due to a point charge is given as follows: E → = k Q s o u r c e r 2 r ^ …… (1) Here, E is the electric field, Q is the charge r is the separation between source point and field point and k is the coulomb’s law constant, and its value is 9 × 10 9 N ⋅ m 2 / C 2 . Consider a ring of radius R and charge Q is distributed over the ring. Let us consider a small element on the ring having length. Now consider a point P above the mid-point of the ring where the electric field is to be found. Let Z is the distance between the point P and the center of the ring and r is the distance between the point P and the elemental point on the ring. Let λ is a linear charge density of the ring and expressed as given below: λ = Q L And also the charge density on the elemental area is given as follows: λ = d q d x …… (2) Here, L is the length of the small elemental area of the ring and written in form of radius as given below: L = 2 π R Now substitute, it in the above equation- λ = Q 2 π R …… (3) Given: z ≪ R z ≫ R Formula used: E → = k Q s o u r c e r 2 r ^ Calculation: Now substitute equation (3) in (2) as given below: d q = Q 2 π R d x Now the electric field due to charge element as given below: d E = k d q r 2 …… (4) Here, by using the Pythagoras theorem is r given as below: r = R 2 + z 2 Now substitute this value and d q = Q 2 π R d x in above equation (4) as given below: d E = k ( Q 2 π R ) d x ( R 2 + z 2 ) 2 …… (5) The sine components of the electric field will be cancelled. Thus, the net electric field at point P is only due to cosine components

Physics for Scientists and Engineers: A Strategic Approach, Vol. 1 (Chs 1-21) (4th Edition)

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ISBN: 9780134110684

Author: Randall D. Knight (Professor Emeritus)

Publisher: PEARSON

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Electric Charges and Fields

One of the fundamental properties is the electromagnetic property. Charge cannot be destroyed by any process and this contributes formally to the law of charge conservation.

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Chapter 23, Problem 45EAP

To determine

Electric field of a ring of charge has expected behavior when z≪R and when z≫R on-axis.

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Chapter 23, Problem 44EAP

Chapter 23, Problem 46EAP

Chapter 23 Solutions

Physics for Scientists and Engineers: A Strategic Approach, Vol. 1 (Chs 1-21) (4th Edition)

Ch. 23 - l. You've been assigned the task of determining...Ch. 23 - Reproduce FIGURE Q23.2 on your paper. For each...Ch. 23 - Rank in order, from largest to smallest, the...Ch. 23 - A small segment of wire in FIGURE Q23.4 contains...Ch. 23 - An electron experiences a force of magnitude F...Ch. 23 - FIGURE Q23.6 shows a hollow soda straw that has...Ch. 23 - The irregularly shaped area of charge in FIGURE...Ch. 23 - A circular disk has surface charge density 8...Ch. 23 - A sphere of radius R has charge Q . The electric...Ch. 23 - The ball in FIGURE Q23.10 is suspended from a...

Ch. 23 - Rank in order, from largest to smallest, the...Ch. 23 - A parallel-plate capacitor consists of two square...Ch. 23 - A small object is released at point 3 in the...Ch. 23 - A proton and an electron are released from rest in...Ch. 23 - Three charges are placed at the comers of the...Ch. 23 - l. What are the strength and direction of the...Ch. 23 - What are the strength and direction of the...Ch. 23 - What are the strength and direction of the...Ch. 23 - What are the strength and direction of the...Ch. 23 - An electric dipole is formed from two charges, q ,...Ch. 23 - An electric dipole is formed from ± 1.0 nC charges...Ch. 23 - An electret is similar to a magnet, but rather...Ch. 23 - The electric field strength 10.0 cm from a very...Ch. 23 - A 10-cm-long thin glass rod uniformly charged to...Ch. 23 - Two 10-cm-long thin glass rods uniformly charged...Ch. 23 - A small glass bead charged to + 6.0 nC is in the...Ch. 23 - The electric field 5.0 cm from a very long charged...Ch. 23 - A 12-cm-long thin rod has the nonuniform charge...Ch. 23 - Two charged rings face each other, 20 cm apart....Ch. 23 - Two 10-cm-diameter charged rings face each other,...Ch. 23 - Two charged disks face each other, 20 cm apart....Ch. 23 - The electric field strength 2.0 cm from the...Ch. 23 - A 20cm20cm cm horizontal metal electrode is...Ch. 23 - Two 2.0-cm-diameter insulating spheres have a 6.0...Ch. 23 - You've hung two very large sheets of plastic...Ch. 23 - A 2.0m X 4.0m flat carpet acquires a uniformly...Ch. 23 - Two circular disks spaced 0.50 mm apart form a...Ch. 23 - A parallel-plate capacitor is formed from two...Ch. 23 - Air "breaks down" when the electric field strength...Ch. 23 - Two parallel plates 1.0 cm apart are equally and...Ch. 23 - a. What is the electric field strength between the...Ch. 23 - Honeybees acquire a charge while flying due to...Ch. 23 - An electron traveling parallel to a uniform...Ch. 23 - The surface charge density on an infinite charged...Ch. 23 - An electron in a vacuum chamber is fired with a...Ch. 23 - A 1.0m -diameter oil droplet (density 900 kg/m3)...Ch. 23 - The permanent electric dipole moment of the water...Ch. 23 - A point charge Q is distance r from a dipole...Ch. 23 - An ammonia molecule (NH3) has a permanent electric...Ch. 23 - What are the strength and direction of the...Ch. 23 - What are the strength and direction of the...Ch. 23 - What are the strength and direction of the...Ch. 23 - Prob. 38EAP Ch. 23 - Prob. 39EAP Ch. 23 - Derive Equation 23.11 for the field Edipolein the...Ch. 23 - FIGURE P23.41 is a cross section of two infinite...Ch. 23 - FIGURE P23.42 is a cross section of two infinite...Ch. 23 - Prob. 43EAP Ch. 23 - Prob. 44EAP Ch. 23 - Prob. 45EAP Ch. 23 - Prob. 46EAP Ch. 23 - Prob. 47EAP Ch. 23 - A plastic rod with linear charge density ? is bent...Ch. 23 - An infinite plane of charge with surface charge...Ch. 23 - A sphere of radius R and surface charge density ?...Ch. 23 - Prob. 51EAP Ch. 23 - An electron is launched at a 45 angle and a speed...Ch. 23 - The two parallel plates in FIGURE P23.53 are 2.0...Ch. 23 - Prob. 54EAP Ch. 23 - Prob. 55EAP Ch. 23 - 56. Your physics assignment is to figure out a way...Ch. 23 - Prob. 57EAP Ch. 23 - Prob. 58EAP Ch. 23 - Prob. 59EAP Ch. 23 - Prob. 60EAP Ch. 23 - Prob. 61EAP Ch. 23 - Prob. 62EAP Ch. 23 - In Problems 63 through 66 you are given the...Ch. 23 - Prob. 64EAP Ch. 23 - Prob. 65EAP Ch. 23 - Prob. 66EAP Ch. 23 - A rod of length L lies along the y-axis with its...Ch. 23 - a. An infinitely long sheet of charge of width L...Ch. 23 - a. An infinitely long sheet of charge of width L...Ch. 23 - Prob. 70EAP Ch. 23 - Prob. 71EAP Ch. 23 - 72. A proton orbits a long charged wire, making ...Ch. 23 - Prob. 73EAP

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