Question

A current element produces a magnetic field in the region surrounding it. At any point in space, the magnetic field produced by this current element points in a direction that is a) radial from the current element to the point in space. b) parallel to the current element. c) perpendicular to the current element and to the radial direction.

Short answer

Answer: The direction of the magnetic field produced by a current element at any point in space is perpendicular to the current element and to the radial direction.

Step-by-step solution

Understand the Biot-Savart Law

The Biot-Savart Law states that the magnetic field dB produced by a small current element (with current I and length dl) at a point in space (P) is given by: dB = \frac{\mu_0}{4\pi} \frac{I (dl \times r)}{r^3}, where µ0 is the permeability of free space, r is the position vector from the current element to the point P, and the cross product (dl × r) indicates that the magnetic field will be perpendicular to both dl and r.

Apply the Right-Hand Rule

To find the direction of the magnetic field produced by the current element, use the right-hand rule. We do this by placing the thumb of our right hand in the direction of the current and the fingers bending in the direction of the position vector r. This way, the direction in which the palm is pushing represents the direction of the magnetic field (outwards for the thumb). By applying the right-hand rule to the Biot-Savart Law formula, we can determine that the magnetic field is perpendicular to both the current element and the radial direction vector. Therefore, the correct option is: c) perpendicular to the current element and to the radial direction.