The magnetic field at the origin due to a current element i d l → placed at a point with vector position r → is

μ 0 i 4 π r → × d l → r 3

μ 0 i 4 π d l → × r → r 2

μ 0 i 4 π r → × d l → r 2

- μ 0 i 4 π d l → × r → r 4

A Conductor (shown in the figure) carrying constant current I is kept in the x - y plane in a uniform magnetic field B → . If F is the magnitude of the total magnetic force acting on the conductor, then the correct statement(s) is (are)

If B → is along y ^ , F ∝ ( L + R )

EASY

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The magnetic permeability is defined as the ratio of Magnetic induction and magnetising field

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Important Questions on Moving Charges and Magnetism

MEDIUM

Physics>Electricity and Magnetism>Moving Charges and Magnetism>Magnetic Field Due to a Current Element, Biot-Savart Law

Two infinite straight wires

A & B, 1 m

apart are carrying currents of

I

and

4 I

respectively. The distance of the points at which the resultant force is zero is

MEDIUM

Physics>Electricity and Magnetism>Moving Charges and Magnetism>Magnetic Field Due to a Current Element, Biot-Savart Law

One of the two identical conducting wires of length

L

is bent in the form of a circular loop and the other one into a circular coil of

N

identical turns. If the same current is passed in both, the ratio of the magnetic field at the centre of the loop

(B_{L})

to that at the centre of the coil

(B_{C}),

i.e.

\frac{B_{L}}{B_{C}}

will be

EASY

Physics>Electricity and Magnetism>Moving Charges and Magnetism>Magnetic Field Due to a Current Element, Biot-Savart Law

The correct Biot-Savart's law in vector form is

MEDIUM

Physics>Electricity and Magnetism>Moving Charges and Magnetism>Magnetic Field Due to a Current Element, Biot-Savart Law

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The figure shows two infinitely long and this parallel wires $P$ and $Q$ placed $0.2 m$ apart perpendicular to the plane of the paper, carrying equal currents of $20 A$ each. Find the magnetic field at a point $R$ , at a distance of $0.2 m$ from both the wires. The symbol $\otimes$ indicates that the current is directed inward.

MEDIUM

Physics>Electricity and Magnetism>Moving Charges and Magnetism>Magnetic Field Due to a Current Element, Biot-Savart Law

A cylindrical conductor of radius

R

is carrying a constant current. The plot of the magnitude of the magnetic field

B

with the distance

d

from the centre of the conductor is correctly represented by the figure.

EASY

Physics>Electricity and Magnetism>Moving Charges and Magnetism>Magnetic Field Due to a Current Element, Biot-Savart Law

The magnetic field at a point due to a current-element is directly proportional to

HARD

Physics>Electricity and Magnetism>Moving Charges and Magnetism>Magnetic Field Due to a Current Element, Biot-Savart Law

A non-conducting thin disc of radius

R

rotates about its axis with an angular velocity

w

. The surface charge density on the disc varies with the distance

r

from the center as

σ (r) = σ_{0} [1 + {(\frac{r}{R})}^{β}]

, where

σ_{0}

and

β

are constants. If the magnetic induction at the center is

B = (\frac{9}{10}) μ_{0} σ_{0} w R

, the value of

β

MEDIUM

Physics>Electricity and Magnetism>Moving Charges and Magnetism>Magnetic Field Due to a Current Element, Biot-Savart Law

Write Bio-Savart law in vector form and mentioned the direction of the magnetic field. Which term in the law work as a vector field and produces a magnetic field? Mention one similarity and one dissimilarity between Bio-Savart law for magnetic field and Coulomb’s law for electrostatics.

MEDIUM

Physics>Electricity and Magnetism>Moving Charges and Magnetism>Magnetic Field Due to a Current Element, Biot-Savart Law

Magnitude of magnetic field (in SI units) at the centre of a hexagonal shape coil of side

10 cm, 50

turns and carrying current

I

(Ampere) in units of

\frac{μ_{0} I}{π}

is :

MEDIUM

Physics>Electricity and Magnetism>Moving Charges and Magnetism>Magnetic Field Due to a Current Element, Biot-Savart Law

In the given figure, the magnetic field at $' O'$ .

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HARD

Physics>Electricity and Magnetism>Moving Charges and Magnetism>Magnetic Field Due to a Current Element, Biot-Savart Law

Explain Biot-Savart law for magnetic field produced due to an element of a current carrying conductor and use it to define the SI unit of current ampere.

MEDIUM

Physics>Electricity and Magnetism>Moving Charges and Magnetism>Magnetic Field Due to a Current Element, Biot-Savart Law

A small current element of length

d l

and carrying current is placed at (1, 1, 0) and is carrying current in '+ z' direction. If magnetic field at origin be

{\vec{B}}_{1}

and at point (2, 2, 0) be

{\vec{B}}_{2}

then:

MEDIUM

Physics>Electricity and Magnetism>Moving Charges and Magnetism>Magnetic Field Due to a Current Element, Biot-Savart Law

State Bio-Savant's law and define unit electric current on the basis of it.

EASY

Physics>Electricity and Magnetism>Moving Charges and Magnetism>Magnetic Field Due to a Current Element, Biot-Savart Law

Two similar insulated wires are bent in the form of a circle of radius $1 cm$ carrying $1 A$ current each in the direction shown as in figure $- I$ and figure $- II$ . Which one will have stronger magnetic field at the centre $O$ ? Justify.

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