A long wire has a charge per unit length of 4.80. (P1) What is the voltage a per

Question

A long wire has a charge per unit length of 4.80. (P1) What is the voltage a perpendicular distance of 12.30 cm away (let the voltage very far away tend to 0)? (P2) A proton is fired at the wire with an initial speed of 58000.00 m/s. It approaches the wire along a perpendicular trajectory. How close does it make it to the wire before it turns around?

Hint: The electric field of the wire is not uniform, so you must use a line integral to compute the voltage. Use conservation of energy to analyze the motion of the proton.

Explanation / Answer

From Gauss's Law, the magnitude of the electric field due to an infinite long wire can be figured as:
E=?/(2pi*epsilon*r)
Put in the given data, we have:
2.53 = (1.51e?10)/(2*3.14159*8.85e?12*r)
Hence r = (1.51e-10)/(2*3.14159*8.85e-12*2.53) = 1.07 (m)

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