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Ronch [10]
3 years ago
6

A disk ring of inner radius a and outer radius b lying on the y − z plane has a uniform surface electric charge density +σ(>

0) on it. (a) Find the electric potential at the point P on the axis of the ring and of a distance x from the center of the ring, taking the zero point of the electric potential at infinity. (b) Find the electric field (both direction and magnitude) at the point P.
Physics
1 answer:
solmaris [256]3 years ago
7 0

Answer:

a)  V = k 2π σ (√(b² + x²) - √ (a² + x²)) ,  

b)  E = - k 2π σ x (1 /√(b² + x²) - 1 /√(a² + x²))

Explanation:

a) The expression for the electric potential is

        V = k ∫ dq / r

For this case, consider the disk formed by a series of concentric rings of radius r and width dr, the distance of each ring to point P

         R = √(x² + r²)

The charge on a ring is

        σ = dq / dA

The area of ​​a ring is

        A = π r

        dA = 2π r dr

So the charge is

        dq = σ  2π r dr

We substitute

       V = k σ 2pi ∫ r dr / √(r² + x²)

We integrate

       V = k 2π σ √(r² + x²)

We evaluate from the lower limit r = a to the upper limit r = b

      V = k 2π σ (√(b² + x²) - √ (a² + x²))

 

b) the electric field and the potential are related

        E = - dV / dx

        E = - k 2π σ (1/2 2x /√(b² + x²) - ½ 2x /√(a² + x²))

        E = - k 2π σ x (1 /√(b² + x²) - 1 /√(a² + x²))

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The given parameters;

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Apply Newton's second law of motion to determine the magnitude of the force on the object.

Due to the position of the object, the magnitude of the force acting on it is calculated as;

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Learn more here: brainly.com/question/19887955

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