Magnetic Field Due to a Current Element, Biot-Savart Law

A long wire with a small current element of length 1 cm is placed at the origin and carries a current of 10 A along the X-axis. Find out the magnitude and direction of the magnetic field due to the element on  the Y-axis at a distance 0.5 m from it.

A circular loop of radius 0.3 cm lies parallel to much bigger circular of radius 20 cm. The centre of the small loop is on the axis of the bigger loop. The distance between their centres is 15 cm. If a current of 2.0 A flows through the smaller loop, then the flux linked with the bigger loop is ______.

State Biot – Savart law.

The magnetic field at the origin due to a current element  \[i d \vec{l}\] placed at a position \[\vec{r}\] is 

(a)\[\frac{\mu_0 i}{4\pi}\frac{d \vec{l} \times \vec{r}}{r^3}\]

(b) \[- \frac{\mu_0 i}{4\pi}\frac{\vec{r} \times d \vec{l}}{r^3}\]

(c) \[\frac{\mu_0 i}{4\pi}\frac{\vec{r} \times d \vec{l}}{r^3}\]

(d) \[- \frac{\mu_0 i}{4\pi}\frac{d \vec{l} \times \vec{r}}{r^3}\] 

State and explain the law used to determine the magnetic field at a point due to a current element. Derive the expression for the magnetic field due to a circular current-carrying loop of radius r at its center.

Biot-Savart law indicates that the moving electrons (velocity v) produce a magnetic field B such that ______.

What does a toroid consist of? Find out the expression for the magnetic field inside a toroid for N turns of the coil having the average radius r and carrying a current I. Show that the magnetic field in the open space inside and exterior to the toroid is zero.

An electric current I flows through a circular loop as shown in Figure 2(b) below. Write an expression and direction for the magnetic field at the centre of the loop at point P.