# Magnetic Field Due to a Circular Arc at the Centre

## Trending Questions

**Q.**A thin conducting ring of radius R is given a charge +Q uniformly distributed over its circumference. The electric field at the centre O of the ring due to the charge on the part AKB of the ring is E. The electric field at the centre due to the charge on the part ACDB of the ring is

- 3E along KO
- E along OK
- E along KO
- 3E along OK

**Q.**

A circular wire loop of radius a carries a total charge Q distributed uniformly over its length. A small length DL of the wire is cut off. Find the electric field at the centre due to the remaining wire.

**Q.**

The magnetic field due to a current carrying circular loop of radius 3 cm at a point on its axis at a distance of 4 cm from the centre is 54 μT. The magnetic field (in μT) at the centre of the loop will be

250

150

125

72

**Q.**Radius of current carrying coil is ′R′. Then ratio of magnetic fields at the centre of the coil to the axial point, which is R√3 distance away from the centre of the coil is

- 1:1
- 1:2
- 1:4
- 8:1

**Q.**A uniformly charged ring with radius 0.5 m has 0.002π m gap. If the ring carries a charge of +1 C, the electric field at the centre is

- 7.5×107 NC−1
- 7.2×107 NC−1
- 6.2×107 NC−1
- 6.5×107 NC−1

**Q.**For the given semi-infinite rod of uniformly distributed line charge, find the net electric field at point P.

- 3.4×105 N/C
- 4.4×105 N/C
- 5.4×105 N/C
- 6.4×105 N/C

**Q.**A bar magnet of length l and magnetic dipole moment M is bent to form an arc which subtends an angle of 120∘ at centre. The new magnetic dipole moment will be

- 3M2π
- 3√3M2π
- 3Mπ
- 2Mπ

**Q.**The magnetic field at the center of current carrying circular loop is B1. The magnetic field at a distance of √3 times radius of the given circular loop from the center on its axis is B2. The value of B1/B2 will

- 5:√3
- 8:1
- 12:√5
- 9:4

**Q.**A wire of length l carries a current i along the X-axis. A magnetic field exists which is given as B=B0(^i+^j+^k) T. Find the magnitude of the magnetic force acting on the wire

- 1√2×B0il
- B0il

- B0il×√2

- 2B0il

**Q.**The ratio of the magnetic field at the centre of a current carrying circular wire and the magnetic field at the centre of a square coil made from the same length of wire will be

- π28√2

- π24√2

- π2√2

- π4√2

**Q.**

In the figure shown there are two semicircles of radii r1 and r2 in which a current i is flowing. The magnetic induction at the centre O will be

**Q.**A cell is connected between the points A and C of a circular conductor ABCD of centre O with angle =60∘. If B1 and B2 are the magnitudes of the magnetic fields at O due to the currents in ABC and ADC respectively, the ratio B1B2 is

- 1
- 5
- 0.2
- 6

**Q.**

Two concentric coils each of radius equal to 2 π cm are placed right angles to each other. If 3A and 4A are the currents flowing through the two coils respectively. The magnetic induction (in Wb m-2) at the center of the coils will be

5×10−5

12×10−5

7×10−5

10−5

**Q.**

State Biot â€“ Savart law. Deduce the expression for the magnetic field at a point on the axis of a current carrying circular loop of radius â€˜Râ€™ at a distance â€˜xâ€™ from the centre. Hence, write the magnetic field at the centre of a loop.

**Q.**The magnetic moment (μ) of an electron revolving around the nucleus, varies with principal quantum number n as,

- μ∝n
- μ∝1n
- μ∝n2
- μ∝1n2

**Q.**

A part of a long wire carrying a current I is bent into a circle of radius r as shown in Fig. The net magnetic field at the centre O of the corcular loop is

μ0I4r

μ0I2πr(π+1)

μ0I2r

μ0I2πr(π−1)

**Q.**The radius of a coil of wire with N turns is 0.22 m and 3.5 A current flows clockwise in the coil as shown. A long straight wire carrying a current 54 A towards the left is located 0.05 meters from the edge of the coil. The magnetic field at the centre of the coil is zero tesla. The number of turns N in the coil are:

**Q.**Due to the flow of current in a circular loop of radius R, the magnetic field produced at the centre of the loop is B. The magnetic moment of the loop is:-

- BR22πμ0
- 2πBR3μ0
- BR22πμ0
- 2πBR2μ0

**Q.**

A straight wire carrying a current of 10 A is bent into a semi-circular arc of radius π cm as shown in Fig. What is the magnitude and direction of the magnetic field at centre 0 of the arc?

10−4 T normal to the plane of the arc and directed outside the page.

10−4 T normal to the plane of the arc and directed into the page.

2×10−4 T parallel to the plane of the arc and directed to the right.

2×10−4 T parallel to the plane of the arc and directed to the left.

**Q.**

Do AC motors have slip rings?

**Q.**

Two concentric coils X and Y of radii 16 cm and 10 cm lie in the same vertical plane containing N-S direction. X has 20 turns and carries 16 A. Y has 25 turns and carries 18 A. X has current in anticlockwise direction and Y has current in clockwise direction for an observer, looking at the coils facing the west. The magnitude of net magnetic field at their common centre is

5π×10−4 T towards west

13π×10−4 T towards east

13π×10−4 T towards west

5π×10−4 T towards east

**Q.**A current of 0.1 A circulates around a coil of 100 turns and having a radius equal to 5 cm. The magnetic field set up at the centre of the coil is

(μ0=4π×10−7 weber/ampere-metre)

- 4π×10−5 tesla
- 2×10−5 tesla
- 8π×10−5 tesla
- 4×10−5 tesla

**Q.**

What is magnetic intensity and magnetizing (magnetic ) field?

**Q.**The magnetic field at the centre of the circular coil carrying current of 4A is

- 8π3×10−5T
- 2π×10−5T
- 8π3×10−4T
- 2π×10−4T

**Q.**

The radius of a circular current-carrying coil is $R$. At what distance from the center of the coil on its axis, the intensity of the magnetic field will be $\frac{1}{2\sqrt{2}}$ times at the center?

**Q.**Three rings, each having equal radius R, are placed mutually perpendicular to each other and each having its centre at the origin of co-ordinate system. If current I is flowing through each ring then the magnitude of the magnetic field at the common centre is

- √3μ0I2R
- zero
- (√2−1)μ0I2R
- (√3−√2)μ0I2R

**Q.**The ratio of magnitude of magnetic field at the centre of a circular current carrying coil to its magnetic moment is N. If the current and radius both were doubled the ratio will become

- 2N
- 4 N
- N8
- N4

**Q.**A 50 turn closely wound circular coil of radius 12 cm carries a current of 2.4 A, the field at center of coil is.

- 6.3×10−3Tesla
- 4.8×10−4Tesla
- 2.4×10−4Tesla
- 6.3×10−4Tesla

**Q.**

A long cylindrical conductor of radius 'a' has two cylindrical cavities each of diameter 'a' through its entire length as shown in the figure. A current I is directed out of the page and is uniform throughout the cross-section of the conductor. The magnetic field at point P1 is

μ0I2πr(2r2+a24r2−a2) to the right

μ0Iπr(2r2+a22r2−a2) to the left

μ0I2π(r2+a2r2−a2) to the right

μ0I2πr(2r2−a24r2−a2) to the left

**Q.**A current I flows in circular arc of wire which subtends an angle θ∘ at the centre. If the radius of the circle is r then the magnetic field B at center is:

- μ0ir
- μ0i2r
- 3μ0i4r
- (θ∘360∘)μ0i2r