Finding B Direction from E and Velocity Direction in EM Waves

Physics · Electromagnetic Waves · NEET

In every electromagnetic wave the direction of travel points along E x B. So to find B, you rotate the electric field vector E so that E x B lines up with the velocity v. In short: v points along E x B, therefore B points along v x E. Memory hook: "V equals E cross B" - fix E and v, then B is whatever makes the cross product come out along v.
E x B rule: velocity v points along E cross BE (+y)B (+z)v (+x)OEBRight-hand set (all at 90 deg)v = E x Bj x k = i, so E(+y) x B(+z) = v(+x)
The three vectors E, B and v are mutually perpendicular. Velocity v points along E x B. With E along +y and B along +z, the cross product j x k = i gives v along +x - the NEET 2018 case.

Your doubts, answered

Is the direction of travel E x B or B x E?

It is always E x B. The velocity (Poynting) direction v is along E x B, in that order. If you flip to B x E you get the exact opposite direction and lose the mark. Fix the order in your head as E first, then B: E cross B gives the way the wave moves.

E is along +y and the wave moves along +x. Is B along +z or -z?

B is along +z. You need E x B to point along +x (the velocity). Check unit vectors: j x k = i, which is +x. Since E is +y (j) and this works with B = +z (k), the answer is +z. If you had guessed -z, then j x (-k) = -i = -x, which is wrong. This is the exact NEET 2018 question.

Does B point along v x E or E x v?

B points along v x E. Start from v = E x B. Cross both sides with E on the left and use the perpendicular geometry: since E, B, v are mutually perpendicular, the shortcut is B is parallel to v x E. Quick check with i, j: if v is +x (i) and E is +y (j), then v x E = i x j = k = +z, matching B = +z.

Why must B be perpendicular to both E and the velocity?

Because EM waves are transverse. NCERT states E and B are perpendicular to each other and both perpendicular to the direction of propagation. So all three (E, B, v) form a right-handed set at 90 degrees to one another. B can never lie along E or along v.

The phase is (kx + wt) not (kx - wt). Does that change the B direction?

Yes, the sign of the phase tells you the travel direction. A (kx - wt) wave moves along +x; a (kx + wt) wave moves along -x. First fix v from the phase sign, then apply v = E x B. In NEET 2025 the phase (5x + 1.5e9 t) meant the wave moved along -x, and only after fixing that could you get the correct B direction.

⚠️ The NEET trap
Using B x E for the propagation direction, or forgetting that (kx + wt) means the wave travels backward, along -x.
Propagation v is always along E x B (E first). Get v from the phase sign first: (kx - wt) is +x, (kx + wt) is -x. Then choose B so that E x B lines up with v.
🧠 Order matters: E then B gives the way it goes. Reverse the order and you reverse the answer.

Real NEET questions

2018

An EM wave is propagating in a medium with velocity v = v i (along +x). The instantaneous oscillating electric field of this EM wave is along the +y axis. Then the direction of the oscillating magnetic field of the EM wave will be along:

A · -y direction
B · +z direction
C · -z direction
D · -x direction
Solution: Rule: propagation direction v is along E x B. Here v is +x (i) and E is +y (j). We need j x B = i (up to a positive factor). Test B = +z (k): j x k = i. This matches +x. So B is along +z. (Check the wrong choice: B = -z gives j x (-k) = -i = -x, which is the wrong way.) Answer: +z direction.
2021

For a plane electromagnetic wave propagating in the +x-direction, which one of the following combinations gives a correct possible pair of directions for the electric field (E) and magnetic field (B) respectively?

A · +j - k , -j - k
B · -j + k , -j + k
C · +j + k , j + k
D · -j + k , -j - k
Solution: Two conditions must hold. First, E must be perpendicular to B, so E . B = 0. Second, E x B must point along +x (i). Test option D: E = -j + k, B = -j - k. Dot product: (-j + k).(-j - k) = (+1) + (-1) = 0, so they are perpendicular - good. Cross product E x B = (-j + k) x (-j - k). Expanding: (-j)x(-j)=0, (-j)x(-k)=+ (j x k)=+i, (k)x(-j)= -(k x j)= -(-i)=+i, (k)x(-k)=0. Sum = 2i, which is along +x. Both conditions pass, so option D is correct.

Solved Electromagnetic Waves NEET PYQs

Try the real previous-year questions from this chapter — each with the answer and a full solution.

See all 20 Electromagnetic Waves NEET PYQs ›
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Frequently asked

What is the quickest rule to find B direction in an EM wave?

Use B along v x E. Since v = E x B, rearranging for perpendicular vectors gives B parallel to v x E. Plug in unit vectors i, j, k and read off the answer.

Are E, B and v always mutually perpendicular?

Yes. EM waves are transverse, so E is perpendicular to B, and both are perpendicular to the propagation direction v. They form a right-handed set.

How do I read the travel direction from the wave equation?

Look at the phase sign. A term like (kx - wt) means the wave travels along +x. A term like (kx + wt) means it travels along -x. Fix v from this before applying E x B.

Does the medium change the direction rule?

No. Whether in vacuum or in a medium, v is still along E x B and the three vectors stay mutually perpendicular. Only the speed changes, not the direction relationship.

What if E and B are given as combinations like -j + k?

Check two things: E . B = 0 (perpendicular) and E x B along the given travel direction. This is exactly how NEET 2021 tested it - only the pair passing both tests is correct.