A 5 volt battery is attached to a resistor that is 100 m away. The wire runs in

Question

A 5 volt battery is attached to a resistor that is 100 m away.   The wire runs in a straight line to the resistor, then a wire is run back to the battery parallel to the first wire.   Where the wires are parallel they are 2 cm apart.       

(A) If 0.05 amps is flowing through the wire, how big is the resistor?  
(B) How large is the magnetic field that is midway between the wires (and 50 m from the battery)?  
(C) If I attach another resistor in parallel with the first, explain what happens to the current in the wire. (No calculation is required.

Explanation / Answer

here,

Volatge, V = 5 V

Distance between wire, d = 2 cm = 0.02 m

Distance to wire, D = 100 m

Distance to midpoint, d = 100/2 = 50 m

Current in wire, I = 0.05 A

Part a:
From ohms Law, Resistance, R = V/I = 5/0.05 = 100 ohms

Part b:
Magnatic field at midpoint,
B = uo*I/(2*pi*d)
B = 4*pi*10^-7*0.05/(2*pi*50)
B = 2*10^-10 T

Part c:

Since now same resistance connected in parallel,
Req = 100 *100/(100 + 100) = 50 ohms

New current, In = V/R = 5/50 = 0.1 A

Current will be doubled.

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