A) Two long, straight wires are parallel and are separated by a distance of d =

Question

A) Two long, straight wires are parallel and are separated by a distance of d = 0.270 m. The top wire in the sketch carries current I1 = 3.30 A , toward the right, and the bottom wire carries current I2 = 5.60 A , also to the right. At point P, midway between the two wires, what is the magnitude?

B) A circular loop and a long, straight wire carry currents as shown in the figure below. The current in the wire is I1 = 10.0 A, toward the right in the sketch. The current in the loop is I2 = 4.00 A and is counterclockwise. The radius of the loop is R = 0.160 m and the point on the loop closest to the long, straight wire is d = 0.0800 m from the wire, as shown in the sketch. What are the magnitude and direction of the resultant magnetic field at the center of the loop (point P)?

Magnitude? direction?

C) The long, straight, and closely-wound solenoid shown in the figure below has length L = 0.500 m, 350 turns of wire and the radius of each turn is R = 1.70 cm. The solenoid is connected to a 64.0-V battery and the current I in the solenoid is 6.70 A. What is the magnitude of the resultant magnetic field at a point inside the solenoid, near the center (point P)?

Explanation / Answer

A) The field direction follows concentric circles around the wire.
Between wires with same current directions the field lines from both wires have the opposite direction .. the net field is the substruction of the individual fields each at a distance .. d = 0.270/2 = 0.135m m (distance to the mid-point)
(separation = 0.270m)

Field at distance (d) from a single wire is given by .. B = .i / 2d
(i = current .. i1=3.30A, i2=5.60A)

B1 = .3.30 / 20.002 .. .. B2 = .5.60 / 20.002

Net field, midway between the wires is

Bn = B2 - B1 = { / 2x0.135} x (5.60-3.30)

Bn = {4x10^-7 / 2x0.135} x 2.3

or, Bn = 3.407x10^-6 T...............................................ans

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