Two long straight wires pass through the middle of the picture. Wire 1 carries a

Question

Two long straight wires pass through the middle of the picture. Wire 1 carries a current up, while wire 2 (perpendicular to wire 1) carries a current to the right. Four points are shown, labelled P, Q, R, and S. The ratio of the current in wire 1 to the current in wire 2 is 4. Defining out of the screen to be positive for magnetic field, we can say that the net field at point S is -B (negative, because it is into the screen). In terms of B, what is the net magnetic field at point P? (Do not include the Bin the answer box below.) Note that this is equivalent to asking for the ratio of the field at P to the field at S. ____ B In terms of B, what is the net magnetic field at point Q? (Do not include the B in the answer box below.) ____ B Now, let's figure out what B represents, in units of teslas. Note that this answer should be positive. If the current in wire 2 is 3 A, and each small square in the picture measures 2 cm times 2 cm, what is B? _____ T

Explanation / Answer

let the current in wire 1 be 4I so current in wire 2 will be I

magnetic field due to current carrying wire = k * I / r

magnetic field at S = -k * I / 1 - k * 4I / 1

-B = -5kI

kI = B/5

magnetic field at P = -k * 4I / 1 + KI / 2

magnetic field at P = -3.5kI

magnetic field at P = -3.5 * B / 5

magnetic field at P = -0.7B

magnetic field at Q = k * 4I / 3 + KI / 1

magnetic field at Q = 7kI / 3

magnetic field at Q = 7B/15

magnetic field at Q = 0.467B

B = 5kI / 0.02

B = 5 * 2 * 10^-7 * 3 / 0.02

B = 0.0005 T

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