Electricity and Magnetism

Charges and Their Interactions

Problem solving - charges and fields

         

A homogeneous ball with mass m=1 gm=1 ~\mbox{g} and total charge q=103 Cq=10^{-3}~\mbox{C} (uniformly distributed) is placed on a horizontal xyxy-plane. The ball starts rolling without slipping under the influence of a uniform electrostatic field E=(E,0,0)\vec{E}=(E,0,0) with E=1 V/m.E=1~ \mbox{V/m}. Find the acceleration in meters per second squared of the center of mass of the ball.

If a point charge Q=3 C  Q = -3 \text{ C } with mass m=1 kg m = 1 \text{ kg} is put at point PP which is at a distance of z=9 m z = 9 \text{ m} above the midpoint between two equal charges q=25×1012 C , q = 25 \times 10^{-12} \text{ C }, at a distance of 2d=24 m 2d =24 \text{ m} apart, the point charge will be move to point O.O. If the speed of the point charge at point OO can be expressed as v=ab m/s, v = \sqrt{\frac{a}{b}} \text{ m/s}, where aa and bb are coprime positive integers, what is the value of a+b?a+b?

Let π3, \pi \approx 3, and the permitivity of free space ϵ09×1012C2N*m2. \epsilon_0 \approx 9\times 10^{-12} \frac{\text{C}^2}{\text{N*m}^2}.

There is a point charge with mass m=1 kg m = 1 \text{ kg} and charge q=9×106 C  q = -9\times 10^{-6} \text{ C } on a uniformly charged sphere with charge Q=9×106 C  Q = 9\times 10^{-6} \text{ C } and radius R=1 m R = 1 \text{ m}. As shown in the above diagram, there is a hole on the sphere, so the point charge can move into the hole. If the period of the point charge can be expressed as T=2πab s, T = 2\pi \sqrt{\frac{a}{b}} \text{ s}, where aa and bb are coprime positive integers, what is the value of a+b?a+b?

Let π3, \pi \approx 3, and the permitivity of free space ϵ09×1012C2Nm2. \epsilon_0 \approx 9\times 10^{-12} \frac{\text{C}^2}{\text{Nm}^2}.

A point particle with mass m=1 kg m = 1 \text{ kg} and charge q=7×106 C  q = -7\times 10^{-6} \text{ C } is rotating around another point particle with charge Q=7×106 C  Q = 7\times 10^{-6} \text{ C } ,which is fixed at the center, with radius r=2 m r = 2 \text{ m}. If the speed of the circular motion can be expressed as v=ab m/s, v = \sqrt{\frac{a}{b}} \text{ m/s}, where aa and bb are coprime positive integers, what is the value of a+b?a+b?

Let π3, \pi \approx 3, and the permitivity of free space ϵ09×1012C2N*m2. \epsilon_0 \approx 9\times 10^{-12} \frac{\text{C}^2}{\text{N*m}^2}.

The potential at point PP which is at a distance of z=6 m z = 6 \text{ m} above the midpoint between two equal charges q=500×1012 C  q = 500 \times 10^{-12} \text{ C } , at a distance of 2d=16 m 2d =16 \text{ m} apart, can be expressed as U=ab J/C, U = \frac{a}{b} \text{ J/C}, where aa and bb are coprime positive integers. What is the value of a+b?a+b?

Let π3, \pi \approx 3, and the permitivity of free space ϵ09×1012C2N*m2. \epsilon_0 \approx 9\times 10^{-12} \frac{\text{C}^2}{\text{N*m}^2}.

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