The two wires shown carry currents of 4.00 A and 8.00 A in opposite directions a
ID: 2280647 • Letter: T
Question
The two wires shown carry currents of 4.00 A
and 8.00 A in opposite directions and are separated by 20.0 cm.
a. Find the magnitude of the force per unit length each wire exerts on the other. Is this force attractive or repulsive.
b. Find the direction and magnitude of the net magnetic field
at a point midway between the wires;
at point P1, 15.0 cm to the right of the wire on the right; and
at point P2, 25.0 cm to the left of the wire on the left.
c. Find the magnitude and direction of the force on
a 6.0 nC charge placed at point P1 and moving to the left at 1.5 x 106 m/s, and
a -4.5 nC charge placed at point P2 and moving toward the top of the page at 2 x 105 m/s.
Explanation / Answer
a)
F = mue*i1*i2*L/(2*pi*d)
F/L = mue*i1*i2/(2*pi*d)
= 2*10^-7*4*8/0.2
= 3.2*10^-5 N
The force is repulsive force.
b)
i) Bnet = mue*i1/(2*pi*r1) + mue*i2/(2*pi*r2)
= 2*10^-7*4/0.1 + 2*10^-7*8/0.1
= 2.4*10^-5 T
ii)
Bnet = mue*i2/(2*pi*r2) - mue*i1/(2*pi*r1)
= 2*10^-7*8/0.15 - 2*10^-7*4/(0.2+0.15)
= 8.38*10^-6 T (out of the page)
iii)
Bnet = mue*i1/(2*pi*r1) - mue*i2/(2*pi*r2)
= 2*10^-7*4/0.25 - 2*10^-7*8/(0.2+0.25)
= 3.56*10^-6 T (in to the page)
c)
i) F = q*v*B = 6*10^-9*1.5*10^6*8.38*10^-6 = 7.542*10^-8 N
direction upward
ii) F = q*v*B = 4.5*10^-9*2*10^5*3.56*10^-6 = 3.204*10^-9 N
direction towards right
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