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Conservative nature of Electric fields

         

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

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

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

Two identical charges with charge \( q= 4 \times 10^{-4} \text{ C} \) and mass \( m = 3 \text{ g} \) are fixed \( r =1.2 \text{ cm} \) 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 \( \epsilon_0 = 8.9 \times 10^{-12} \text{ F/m}. \)

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

A \( V_b = 12 \text{ V} \) battery is connected to two parallel plates separated by a distance of \( d_p = 6 \text{ cm}. \) This creates a uniform electric field between the two plates. If a point charge \( Q = 5 \text{ C} \) 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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