A positive point charge Q₁ = 2.5 x 10^-5 C is fixed at the origin of coordinates, and a negative point charge Q₂ = -5.0 x 10^-8 C is fixed to the 𝓍 axis at 𝓍 = +3.2 m. Find the location of the place(s) along the 𝓍 axis where the electric field due to these two charges is zero.

Two positive point charges are a fixed distance apart. The sum of their charges is Qₜ. What charge must each have in order to

(a) maximize the electric force between them, and

(b) minimize it?

(II) At each corner of a square of side ℓ there are point charges of magnitude Q, 2Q, 3Q, and 4Q (Fig. 21–57). Determine the magnitude and direction of the force on the charge 2Q.

CALC A uniform electric field’s strength is increasing with time as $E=(1.5\times {10}^4+(5.0\times {10}^{10}{\text{s}}^{-1}\left)t\right)\text{N/C}$. A proton is released in the field from rest at t = 0. What is the proton’s speed 1.0 μs later?

Two equal point charges 2.5 cm apart, both initially neutral, are being charged at the rate of 5.0 nC/s. At what rate (N/s) is the force between them increasing 1.0 s after charging begins?

Two 10-cm-diameter charged rings face each other, 20 cm apart. The left ring is charged to −20 nC and the right ring is charged to +20 nC. What is the force on a proton at the midpoint?