Conservative nature of Electric fields

         

A constant electric field E=5 V/m E = 5 \text{ V/m} exists, as depicted in the above figure. A Q=5×103 C Q= 5 \times 10^{-3} \text{ C} charge of mass m=4 g, m = 4 \text{ g}, initially at rest at xa=1 m, x_a = - 1 \text { m}, is released. What is its approximate speed at xb=2 m? x_b = 2 \text{ m}?

A charge of q=4.0 C, q = 4.0 \text{ C}, initially away from a fixed point charge of 1.0 nC 1.0 \text{ nC} by a distance of r1=7.0 m, r_1 = 7.0 \text{ m}, moves closer to a point where the distance is r2=1.0 m.r_2= 1.0 \text{ m}. What is the approximate work done to the charge?

Assume that electric constant is ϵ0=8.9×1012 F/m. \epsilon_0 = 8.9 \times 10^{-12} \text{ F/m}.

Two identical charges with charge q=4×107 C q= 4 \times 10^{-7} \text{ C} and mass m=3 g m = 3 \text{ g} are fixed r=1.2 cm r =1.2 \text{ cm} apart. Another identical charge is shot from infinity and stops midway between the two. What is its approximate initial speed?

Assume that electric constant is ϵ0=8.9×1012 F/m. \epsilon_0 = 8.9 \times 10^{-12} \text{ F/m}.

A charge of 3.0×103 C - 3.0 \times 10^{-3} \text{ C} is moved through a potential difference of 3.0 V. 3.0 \text{ V}. Calculate the work done on the charge.

A Vb=12 V V_b = 12 \text{ V} battery is connected to two parallel plates separated by a distance of dp=6 cm. d_p = 6 \text{ cm}. This creates a uniform electric field between the two plates. If a point charge Q=5 C Q = 5 \text{ C} is put in the middle between the plates, what is the kinetic energy of the charge when it touches the plates?

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