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September 12, 2008
PHY2054 Discussion-Fall ‘08
Quiz 2 (Chapter 15.7-16.3)
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UFID:
*1. (5pts) The dome of a Van de Graaff generator receives a charge of 3.00×10-4 C. Find the strength
of the electric field at the outer surface of the dome, assuming the dome is a conducting spherical
shell with a radius of 1.50 m.
We apply Gauss’s law to a spherical Gaussian surface of radius 1.5 m. Since the entire charge is
inside the Gaussian surface, we have
E(4πr²) = Q/ε0 ⇒ E = Q/(4πε0r²) = kQ/r² = 8.99×109×3×10-4/1.5² = 1.20×106 N/C
*2. (5pts) An electric field with an intensity of 5.00 kN/C is applied along the x-axis. What is the
electric flux through a rectangular plane 0.400 m wide and 0.600 long if the plane contains y-axis
and its normal makes an angle of 60.0˚ with the x-axis.
Using the definition of electric flux, we have
Φ = EAcosθ = 5×103×(0.4×0.6)×cos60˚ = 6.00×102 N m²/C
***3. (5pts) A 2.00-kg block is attached to the lower end of a spring lying along a 30.0˚ incline. The
coefficient of kinetic friction between the incline and the block is 0.25. The spring has a force
constant of 150 N/m and it is fixed at the upper end. The block is charged and the system is
immersed in a uniform electric field with an intensity of 6.00×105 N/C directed vertically downward.
The block is released from rest when the spring is unstretched. If the block slides 0.200 m down the
incline before it turns around for the first time, what is the charge given to the block?
We take +x-axis along the incline and +y perpendicular to the incline. Since the block does not move
in the y direction, the normal force is expressed as
ΣFy = 0 ⇒ n-mgcosθ-qEcosθ = 0 ⇒ n = (mg+qE)cosθ
Applying work-energy theorem to the system, we have
Wnc = ΔE ⇒ -μ(mg+qE)cosθΔx = (1/2)kΔx²-mgsinθΔx-qEsinθΔx
⇒ qE(sinθ-μcosθ) = (1/2)kΔx-mg(sinθ-μcosθ)
⇒ q = kΔx/[2E(sinθ-μcosθ)]-mg/E
= 150×0.2/[2×6×105(sin30˚-0.25cos30˚)]-2×9.8/(6×105) = 5.55×10-5 C
**4. (5pts) Three charges q1 =2.00 μC, q2 = -4.00 μC and q3 = 6.00 μC are placed at three vertices of
a rectangle, q1 at the upper left corner, q2 at the lower left and q3 at the lower right. q1 and q2 are
separated by 0.300 m and q2 and q3 are separated by 0.400 m. What is the work required to move a
-8.00-μC charge from infinity to the fourth vertex?
The length of the diagonal is
r2 = √r1²+r3²) = √(0.3²+0.4²) = 0.5 m
The required work is work done by an external force equal and opposite to the electric force. Thus
we have,
Wex = -Wel = ΔPE = qΔV = qk(q1/r1+q2/r2+q3/r3)
= -8×10-6×8.99×109×(2/0.4-4/0.5+6/0.3)×10-6 = -1.22 J