Physics · Magnetic Effects of Current · Video solution

Two infinitely long straight parallel wires perpendicular to the plane of the paper are 5 m…

Question

Two infinitely long straight parallel wires perpendicular to the plane of the paper are 5 m apart. One of the wires, P carries current I out of the plane of the paper and the other, Q carries the current I into the plane of paper. The magnetic field B at the origin O of the coordinate system with x and y axes as perpendicular and parallel to PQ, respectively, is [Given OP=4 m and OQ=3 m] (a) fracμ₀I2π(hati−3/5hatj) (b) fracμ₀I5π(hati−7/24hatj) (c) fracμ₀I5π(-hati+3/8hatj) (d) fracμ₀I24π(2hati+3hatj)

Answer

(b) fracμ₀I5π(hati−7/24hatj)

Concept: Magnetic field due to current

Step-by-step solution

  1. 1. Magnetic field from P

    B = μ₀I / 2πr • r_P = 4m • Direction: Right-hand rule

    BP=μ0I2π(4)B_P = \frac{\mu_0 I}{2\pi (4)}

  2. 2. Magnetic field from Q

    r_Q = 3m • Direction: Right-hand rule

    BQ=μ0I2π(3)B_Q = \frac{\mu_0 I}{2\pi (3)}

  3. 3. Resolve into components

    BP:−xdirection•BQ:+ydirectionB_P: -x direction • B_Q: +y direction

    BP=−μ0I8πi^B_P = -\frac{\mu_0 I}{8\pi} \hat{i}

  4. 4. Resultant magnetic field

    B_total = B_P + B_Q • Add vector components

    Btotal=BP+BQB_{total} = B_P + B_Q

  5. 5. Yaad rakho / Key takeaway

    Use right-hand rule for direction, then vector addition for total field.

Remember

Use right-hand rule for direction, then vector addition for total field.

Common mistake

Incorrectly applying the right-hand rule or vector addition.

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