Electric field and Gauss's Law

Three charges that can move only along the x-axis are placed successively with equal spacing are found to be equilibrium. Which of the following holds?

• q₁ and q₃ must have the same sign

• q₁ and q₃ must have the same amount

• q₂ = q₁/4

• q₂=4q₁

A 1m long wire with uniform charge density creates some electric field at 1m distance from its center. By what factor does the electric field change if the wire is replaced by an infinitely long one with same charge density?

A uniformly charged rod extending the left edge of the unit square creates and electric field E₁ at upper corner. If the rod is placed to the bottom edge of the square, which of the following is true about the new electric field E₂ at the same corner?

• E_2x = E_1x

  E_2y = E_1y

• E_2x = E_1y

  E_2y = E_1x

An electric dipole p = 2 nCm is placed at 150^o to a uniform electric field E = 1 V/m. How much work in nJ does the electric field until the dipole reaches to equilibrium?

Gauss's law in electrostatics is about...

• total electric field on a closed surface

• total electric flux through a closed surface

• total electric field in a volume

• total electric flux in a volume

Which of the following is true for a conducting spherical shell?

I) A charge outside the shell can create E inside the shell.

II) A charge inside the shell can create E outside the shell.

III) If the charge inside is off-centered, the induced charge at the inner surface is non-uniform.

IV) If the charge inside is off-centered, the induced charge at the outer surface is non-uniform.

• I

• II

• III

• IV

Two concentric conducting spherical shells have radii R and 3R and charges +2Q, +5Q, respectively. Let E be the electric field at r = 5R. A wire is connected from inner to the outer sphere. What is the new electric field at r=R in terms of E?

• 1

• 7/4

• 3

• 21/4

• 3/9

• 4/9

• 6/9

• 12/9

A conducting spherical shell of radius 3R has charge Q distributed uniformly. It is brought in contact briefly to a isolated neutral spherical shell of radius R. We assume that the uniform charge distribution is maintained during contact as well. What is the charge on the small spherical shell after they are separated?

• 3Q/4

• Q/2

• Q/3

• Q/4

A half ring is charged alternating in 4 equal arc lengths as shown. The net electric field at the origin is

• in x direction

• in -x direction

• in y direction

• in -y direction

• zero