Advertisements
Advertisements
प्रश्न
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) \[- \frac{\mu_0 i}{4\pi}\frac{d \vec{l} \times \vec{r}}{r^3}\]
उत्तर
(a) \[\frac{\mu_0 i}{4\pi}\frac{d \vec{l} \times \vec{r}}{r^3}\]
(b) \[- \frac{\mu_0 i}{4\pi}\frac{\vec{r} \times d \vec{l}}{r^3}\]
The magnetic field at the origin due to current element \[i d \vec{l}\] placed at a position \[\vec{r}\] is given by \[d \vec{B} = \frac{\mu_o}{4\pi}i\frac{\vec{r} \times d \vec{l}}{r^3}\]
According to the cross product property,
\[\vec{A} \times \vec{B} = - \vec{B} \times \vec{A} \]
\[ \Rightarrow d \vec{B} = - \frac{\mu_o}{4\pi}i\frac{\vec{r} \times \vec{dl}}{r^3}\]
APPEARS IN
संबंधित प्रश्न
State Biot – Savart law.
Express Biot – Savart law in the vector form.
A proton goes undeflected in a crossed electric and magnetic field (the fields are perpendicular to each other) at a speed of 2.0 × 105 m s−1. The velocity is perpendicular to both the fields. When the electric field is switched off, the proton moves along a circle of radius 4.0 cm. Find the magnitudes of the electric and magnetic fields. Take the mass of the proton = 1.6 × 10−27 kg
A long, vertical wire carrying a current of 10 A in the upward direction is placed in a region where a horizontal magnetic field of magnitude 2.0 × 10−3 T exists from south to north. Find the point where the resultant magnetic field is zero.
A wire of length l is bent in the form of an equilateral triangle and carries an electric current i. (a) Find the magnetic field B at the centre. (b) If the wire is bent in the form of a square, what would be the value of B at the centre?
A wire of length l is bent in the form of an equilateral triangle and carries an electric current i. Find the magnetic field B at the centre.
A regular polygon of n sides is formed by bending a wire of total length 2πr which carries a current i. (a) Find the magnetic filed B at the centre of the polygon. (b) By letting n → ∞, deduce the expression for the magnetic field at the centre of a circular current.
State and explain the law used to determine 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 centre.
State Biot Savart law.
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.
Derive the expression for the magnetic field due to a current-carrying coil of radius r at a distance x from the center along the X-axis.
A straight wire carrying a current of 5 A is bent into a semicircular arc radius 2 cm as shown in the figure. Find the magnitude and direction of the magnetic field at the center of the arc
- both are long range and inversely proportional to the square of distance from the source to the point of interest.
-
both are linear in source.
-
both are produced by scalar sources.
-
both follow principle of superposition.
Biot-Savart law indicates that the moving electrons velocity (V) produce a magnetic field B such that ______.
Biot-Sawart law indicates that the moving electrons (velocity `overset(->)("v")`) produce a magnetic field B such that
The magnetic field at any point on the axis of a current element is ______
Using Biot-Savart law, show that magnetic flux density 'B' at the centre of a current carrying circular coil of radius R is given by: `B = ("μ"_0I)/(2R)` where the terms have their usual meaning.
