Physics · Moving Charges And Magnetism · NEET
Set up a 3x3 determinant. Row 1 = i, j, k. Row 2 = velocity components (vx, vy, vz). Row 3 = field components (Bx, By, Bz). Then: i-part = (vy·Bz - vz·By), j-part = -(vx·Bz - vz·Bx), k-part = (vx·By - vy·Bx). Multiply the whole thing by q. Example: v = 2i + 4j + 6k, B = -6i - 6j - 8k gives i-part = (4)(-8) - (6)(-6) = 4. Always cross-multiply diagonally and subtract.
For F = q(v x B), the velocity v goes in the SECOND row (just below i, j, k) and B goes in the THIRD row. Order matters because cross product is not commutative: v x B = -(B x v). If you swap the rows, every sign flips and your force points the wrong way. Rule: the thing being multiplied first (v) sits on top.
When you expand a determinant, the cofactor signs alternate + - +. So the i-term is positive, the j-term carries a minus, and the k-term is positive again. Students who forget this minus get the j-component with the wrong sign and pick the wrong option. Always write it as j-part = -(vx·Bz - vz·Bx).
In NEET you usually do NOT solve the messy equations. Instead, take q = 1 so F = v x B, then test each option. Plug the given B option into the determinant, expand, and see which one reproduces the given F exactly. This 'plug and check' is faster and safer than algebra under exam pressure.
No. They are equal in magnitude but opposite in direction: v x B = -(B x v). This is the number-one silent mistake. If a question writes F = qv x B, keep v on top. Never reorder to make the arithmetic 'nicer' - you will flip the sign of the force.
In the product F = q(v x B) = q(vx i + vy j + vz k) x (Bx i + By j + Bz k), for q = 1 and v = 2i + 4j + 6k and F = 4i - 20j + 12k, what is the complete expression for B?
Try the real previous-year questions from this chapter — each with the answer and a full solution.
Set q = 1 (or pull q out), then plug each option's B into the i, j, k determinant and check which reproduces the given force. Plug-and-check beats algebra.
Not for component problems. You just match the three components (i, j, k) with the given force vector. Magnitude questions are a different type.
That is a clue: it means v and B are arranged so that one determinant term cancels. Use it to eliminate options quickly instead of expanding fully.
Yes. A negative q (like an electron) flips the direction of F. Keep q with its sign when you multiply the determinant result.
Here you only handle the magnetic term q(v x B). In a velocity selector you balance the electric force qE against qvB so net force is zero - that is the next concept to study.
