Consider two long wires with current I_1 = 6.6 A and I_2 = 1.2 A as shown in the

Question

Consider two long wires with current I_1 = 6.6 A and I_2 = 1.2 A as shown in the figure. Let d = 0.85 m, a = 1.9 m. Express the magnitude of the magnetic field at A created by current I_1, B_A1, in terms of I_1 and d. What is the direction of B_A1? Express the magnitude of the magnetic field at A created by current I_2, B_A2, in terms of I_2 and d. What is the direction of B_A2? Express the total magnetic field at A created by current I_1, and I_2, B_A in terms of I_1, I_2, and d. Take out of the screen as the positive direction. B_A = (mu_0 I_1/(pi d)) Calculate the numerical value of B_A in Tesla. What is the direction of B_A? Express the magnitude of the magnetic field at B created by current I_1, B_B1, in terms of I_1 and a. What is the direction of B_B1? Express the magnitude of the magnetic field at B created by current I_2, B_B2, in terms of I_2, a and d. What is the direction of B_B2? Express the total magnetic field at B created by current I_1 and I_2, B_B, in terms of I_1, I_2, a, and d. Use out of the page as the positive direction. Calculate the numerical value of B_B in Tesla. What is the direction of B_B?

Explanation / Answer

Given that
I1 = 6.6 A
I2 = 1.2 A
d = 0.85 m
a = 1.9 m

Part (a)

Ba1 = (u0*i1)/(2*pi*(d/2))

= (u0*i1)/(pi*d)

= (4*3.14*10^-7*(6.6)/(3.14*0.85)

B = 3.105*10^-6 T

Part (b)

into the page

Part (c)

Ba2 = (u0*i2)/(2*pi*(d/2))

= (u0*i2)/(pi*d)

= (4*3.14*10^-7)*(1.2)/(3.14*0.85)

B = 5.647*10^-6 T

Part (d)

out of the page

Part (e)

Ba = Ba2 - Ba1

= u0*i2/(pi*d) - u0*i1/(pi*d)

= u0*(i2 - i1)/(pi*d)

Part (f)

Ba = (4*3.14*10^-7)*(1.2 - 6.6)/(3.14*0.85)

Ba = - 2.54*10^-6 T

Part (g)

into the page

Part (h)

Bb1 = (u0*i1)/(2*pi*a)

Part (i)

out of the page

Part (j)

Bb2 = (u0*i2)/(2*pi*(a+d))

Part (k)

out of the page

Part (l)

Bb = Bb1 + Bb2

= (u0*i1)/(2*pi*a) + (u0*i2)/(2*pi*(a+d))

Part (m)

Bb = (4*3.14*10^-7)*(6.6)/(2*3.14*0.85) + (4*3.14*10^-7)*(1.2)/(2*3.14*(1.9+0.85))

Bb = 1.640*10^-6 T

Part (n)

out of the page

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