Question:
A negative test charge is moving near a long straight wire carrying a current. The force acting on the test charge is parallel to the direction of the current. The motion of the charge is :
A negative test charge is moving near a long straight wire carrying a current. The force acting on the test charge is parallel to the direction of the current. The motion of the charge is :
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The magnetic field of the wire circles around it, and \(\vec F = q\vec v \times \vec B\) is perpendicular to both \(\vec v\) and \(\vec B\); a force along the wire then needs a radial velocity, whose sign follows from the negative charge.
Updated On: Nov 11, 2026
- away from the wire
- towards the wire
- parallel to the wire along the current
- parallel to the wire opposite to the current
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The Correct Option is B
Solution and Explanation
Take the current along \(+\hat z\) and the charge at \(+x\) from the wire. The field there is \(\vec B = B\,\hat y\) (right hand rule).
The force is given as parallel to the current: \(\vec F = +F\,\hat z\).
For a negative charge \(\vec F = -|q|\,\vec v \times \vec B\), so \(\vec v \times \hat y\) must point along \(-\hat z\).
With \(\vec v = v_x \hat x\): \(\hat x \times \hat y = +\hat z\), so we need \(v_x \lt 0\), i.e. \(\vec v\) along \(-\hat x\).
The charge is at \(+x\) and moves toward \(-x\), i.e. towards the wire.
Answer: (2) towards the wire
The force is given as parallel to the current: \(\vec F = +F\,\hat z\).
For a negative charge \(\vec F = -|q|\,\vec v \times \vec B\), so \(\vec v \times \hat y\) must point along \(-\hat z\).
With \(\vec v = v_x \hat x\): \(\hat x \times \hat y = +\hat z\), so we need \(v_x \lt 0\), i.e. \(\vec v\) along \(-\hat x\).
The charge is at \(+x\) and moves toward \(-x\), i.e. towards the wire.
Answer: (2) towards the wire
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