106-20102-MT1 - Phys 106 First Midterm Examination Page 1...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Phys 106 First Midterm Examination Page 1 Saturday, 02-Apr, 2011 PROBLEM (1) (25 points) A positive charge Q is uniformly distributed over a quarter circle (one fourth of a circle) of radius R . The charged quarter circle is located symmetrically relative to the x axis, as shown in the figure. The point P is at the origin, and is the center of the quarter circle. Express your answers in terms of the given quantities and fundamental constants as needed. ( sin 45 ° = cos45 ° = 2 2 ) x y R Q P 45° R d Q ! d ! ! d ! E dE x dE y (a) (10 pts) Find the magnitude of the x component of the electric field at the point P . See the charge element dQ in the figure above. dQ = ! d ! = Q ( 2 " R 4 ) ( Rd # ) = 2 Qd # " dE = k e dQ R 2 = 2 k e Qd ! " R 2 E x = dE x ¡ = dE cos ! ¢ " /4 " /4 ¡ = 2 k e Q " R 2 cos ! ¢ " /4 " /4 ¡ d ! E x = 2 k e Q ¡ R 2 sin ¢ [ ] ! ! /4 ! /4 = 2 k e Q ! R 2 sin( ! 4 ) ! sin( ! ! 4 ) " # $ % & ' E x = 2 k e Q ! R 2 2 2 ! ( ! 2 2 ) " # $ % & ' = 2 k e Q ! R 2 2 2 + 2 2 " # $ % & ' E x = 2 k e Q 2 ! R 2 or E x = Q 2 2 ¡ 2 ¢ R 2 (b) (5 pts) Find the magnitude of the y component of the electric field at the point P . E y = dE y ¡ = dE sin ! ¢ " /4 " /4 ¡ = 2 k e Q " R 2 sin ! ¢ " /4 " /4 ¡ d ! E y = 2 k e Q ¡ R 2 ! cos ¢ [ ] ! ! /4 ! /4 E y = ! 2 k e Q ! R 2 cos( ! 4 ) ! cos( ! ! 4 ) " # $ % & ' = E y = (c) (5 pts) Using the unit vectors, write down an expression for the net electric field ! E at the point P . ! E = E x ˆ i + E y ˆ j where E y = . ! E = 2 k e Q 2 ! R 2 ˆ i or ! E = Q 2 2 ¡ 2 ¢ R 2 ˆ i (d) (5 pts) If a point charge q is located at x = R 2 , the net electric field at the point P becomes zero. Find the charge q in terms of Q and state whether q is positive or negative. The net electric field at P is ! E = ! E 1 + ! E ¡ , where: ! E 1 = field due to point charge q ! E 2 = field due to charged quarter circle ! E = ! E 1 + ! E ¡ = ! E 1 = ! E ¡ k e q ( R ¡ ) ¡ = ¡ k e Q ¡ ! R ¡ q = Q 2 2 ! q is positive Phys 106 First Midterm Examination Page 2 Saturday, 02-Apr, 2011 PROBLEM (2) (25 points) The spherical region a < r < b carries a positive charge per unit volume ! = A r , where A is a positive constant and r is the distance from the center. A positive point charge Q is located at the center ( r = 0) of the cavity. Express your answers in terms of the given quantities and fundamental constants as needed....
View Full Document

This note was uploaded on 07/28/2011 for the course PHYS 105 at Middle East Technical University.

Page1 / 4

106-20102-MT1 - Phys 106 First Midterm Examination Page 1...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online