Assignment-I
Total Marks- 35; Date of Submission: 07 November 2022 10:00 AM
Show all your works with proper justifications; partial credit will be given if merited.
1. A 2.0 μC point charge and a 4.0 μC point charge are a distance L apart. Where should a
third point charge be placed so that the electric force on that third charge is zero?
2. When a shower is turned on in a closed bathroom, the splashing of the water on the bare
tub can fill the room’s air with negatively charged ions and produce an electric field in the
air as great as 1000 N/C. Consider a bathroom with dimensions 2.5 m × 3.0 m × 2.0 m.
Along the ceiling, floor, and four walls, approximate the electric field in the air as being
directed perpendicular to the surface and as having a uniform magnitude of 600 N/C. Also,
treat those surfaces as forming a closed Gaussian surface around the room’s air. What are
(a) the volume charge density ρ and (b) the number of excess elementary charges e per
cubic meter in the room’s air?
3. A 1.0 cm side square surface in the x-y plane sits in a uniform electric field
𝐸⃗ = 2.0𝑖̂ + 3.0𝑗̂ − 3.0𝑘̂ N/C. Find the electric flux through the square.
4. A solid insulating sphere of radius 𝑅 has a charge +Q distributed uniformly
throughout its volume (the volume charge density 𝜌 is constant). The
insulating sphere is surrounded by a solid spherical conducting shell with inner radius 2𝑅
and outer radius 3𝑅 as shown in the Figure. The conductor is in static equilibrium and has
a zero net charge. What is the magnitude of the electric field at the point 𝑟 = 5𝑅/2 inside
the conductor? What is the magnitude of the electric field at the point 𝑟 = 4𝑅 outside the
conductor?
5. A long, thin, straight wire of length L has a positive charge Q distributed uniformly along
it. Use Gauss’ law to find the expression of electric field created by this wire at a radial
distance r.
6. Figure gives the magnitude of the electric field inside and outside a sphere with a positive
charge distributed uniformly throughout its volume. The scale of the vertical axis is set by
𝐸𝑥 = 5.0 × 107 𝑁/𝐶.What is the charge on the sphere?
7. An electric dipole of dipole moment 5 × 10−18 𝐶. 𝑚 is placed in a uniform electric field
that has a magnitude of 4.0 × 104 N/C. What is the magnitude of the torque on the dipole
when (a) the dipole is aligned with the electric field, (b) the dipole is transverse to
(perpendicular to) the electric field, and (c) the dipole makes an angle of 30º with the
direction of the electric field? (d) Defining the potential energy to be zero when the dipole
is transverse to the electric field, find the potential energy of the dipole for the orientations
specified in Parts (a) and (c).