Old Exams #1

Physics 123 Exam #1 Fall 2002
Do any THREE of the following four questions. X-OUT the question you OMIT.
Note that you will only have two parts per question on yor exams instead of three parts.

1. Two identical negative point-charges –Q are place on the horizontal x-axis. One charge is 52.0 cm to the left of the origin and the other charge is 38.0 cm to the right of the origin. The force on either charge is 460 N.

(A) What is the magnitude of either charge?
Ans:{-203 mC}

(B) What is the direction and magnitude of the electric field at the origin due to both charges?

Ans:{5.91x10⁶ V/m, Right}

Ans:{-8.14x10⁶V}

2. A spherical charge distribution ρ(r) produces a spherical electric field E(r) = a r² where a is a constant equal to 72.0x10³ V/m³.

(A) If a –66.0 nC charge is placed 1.50 m from the origin, what is the magnitude and direction of the electric force acting on the charge?

Ans:{.0107 N, towards the origin}

(B) What is the total charge interior to a sphere of radius 85.0 cm?

Ans:{4.18 mC }

(C) Determine the magnitude of the voltage difference ΔV between a point 85.0 cm from the origin and a point 1.50 m from the origin?

Ans:{66.3 kV}

3. A -41.0 mC charge q₁ is placed at the origin and a +170 mC charge q₂ is placed 190 cm directly above q₁ on the y-axis.

(A) What is the magnitude and direction of the force that charge q₁ exerts on q₂?

Ans:{17.4 N, Down}

(B) What is the magnitude and direction of the electric field due to both charges at a point 68.0 cm above the origin?

Ans:{1.83x10⁶N/C, Down)

(C) How much kinetic energy will charge q₂ have when it reaches the point 68.0 cm above the origin if it is released from rest at 190 cm above the origin and q₁ is anchored to the origin?

Ans:{59.2 J}

4. An infinitely long cylinder with a radius R = 11.0 cm has a uniform surface charge density σ = +61.0 nC/m² on its surface that is fixed in position. The electric potential at distance r from the center of the cylinder is given by

(A) What is the charge per unit length λ on the conducting cylinder?

Ans:{42.2 nC/m}

(B) What is the magnitude and direction of the electric field 48.0 cm from the surface of the conducting cylinder?

Ans:{1.58 kV/m, outwards}

(C) How much work will it take to move a 52.0 mC charge from a distance of 3.00 m to a distance of 1.50 m from the center of the cylinder?

Ans:{27.3 mJ}

Physics 123 Exam #1 Spring 2002

1. Two charge of equal magnitude but opposite signs are placed 28.0 cm from the origin on the y-axis. The positive charge is above the origin and the negative charge is below the origin. If the magnitude of the electric field at the origin is 4.10 kV/m.

(A) What is the direction of the electric field at the origin? Sketch the E-field vector on the figure given.
Ans:{Down}

(B) What is the magnitude of the size of the charge of either charge in microcoulombs ?
Ans:{17.9 nC}

2. A -55.0 mC charge is place 15.0 cm to the left of the origin on the x-axis.

(A) Where (relative to the origin) on the positive x-axis is the electric potential equal to -1,100 kV ?
Ans:{30.0 cm}

(B) What is the electric potential at a point P that is 33.0 cm above the origin on the y-axis ?
Ans:{-1370 kV}

(C) How much work will it take to move a -42.0 mC charge from a 33.0 cm above the origin straight down the y-axis to the origin if the -55.0 mC is fixed in place ?

Ans:{81.2 J}

3. A nonconducting sphere of radius 88.0 cm has total charge of +83.0 nC spread though out the sphere in such a way that the charge distribution is spherical and the electric field is given by E = a/r radial outwards where a = 850 Volts

(A) What is the magnitude and direction of the force on a –44.0 mC charge placed at the surface of the nonconducting sphere?
Ans:{42.5 mN, towards the center}

(B) What is the magnitude of electric potential drop between 60.0 cm from the origin to the surface of the sphere at 88.0 cm?
Ans:{326 V}

4. Two point charges lay on the x- axis. The second point charge has a charge of –35.0 mC and is locked into position at +1.30 m from origin. The first charge has a charge of –4.60 mC and is traveling towards the other charge at 160 m/s. If the first charge has a mass of 190 g and starts out at the origin:

(A) What is force on charge one initially?
Ans:{857 N}

(B) Determine both the electric potential in volts at the location of the first charge due to the second charge initially and the electric potential energy in joules of the first charge initially?
Ans:{-242 kV, 1.11 kJ}