# Magnetic Field Due to Finite Wire

## Trending Questions

**Q.**An infinitely long thin non-conducting wire is parallel to the z-axis and carries a uniform line charge density λ. It pierces a thin non-conducting spherical shell of radius R in such a way that the arc PQ subtends an angle 120∘ at the centre O of the spherical shell, as shown in the figure. The permittivity of free space is ∈0. Which of the following statements is (are) true?

- The electric flux through the shell is √3Rλ/∈0
- The z-component of the electric field is zero at all the points on the surface of the shell
- The electric flux through the shell is √2Rλ/∈0
- The electric field is normal to the surface of the shell at all points

**Q.**The magnetic field at the centre of an equilateral triangular loop of side 2L and carrying a current i is

- 9μ0i4πL
- 3√3μ0i4πL
- 2√3μ0iπL
- 3μ0i4πL

**Q.**

A
short bar magnet of magnetic moment 5.25 Ã— 10^{âˆ’2}
J T^{âˆ’1}
is placed with its axis perpendicular to the earthâ€™s field
direction. At what distance from the centre of the magnet, the
resultant field is inclined at 45Âº with earthâ€™s field on

(a) its normal bisector and (b) its axis. Magnitude of the earthâ€™s field at the place is given to be 0.42 G. Ignore the length of the magnet in comparison to the distances involved.

**Q.**

Two identical moving coil galvanometers have 10 Ω resistance and full scale deflection at 2 μA current. One of them is converted into a voltmeter of 100 mV full scale reading and the other into an Ammeter of 1 mA full scale current using appropriate resistors. These are then used to measure the voltage and current in the Ohm's law experiment with R=1000 Ω resistor by using an ideal cell. Which of the following statement(s) is/are correct?

- The measured value of R will be 978 Ω<R<982 Ω
- The resistance of the ammeter will be 0.02 Ω (round off to 2nd decimal place)
- If the ideal cell is replaced by a cell having internal resistance of 5 Ω then the measured value of R will be more than 1000 Ω
- The resistance of the voltmeter will be 100 kΩ

**Q.**A current i is flowing in a straight conductor of length L. The magnetic field at a point distant L4 from its centre will be

- 4μ0i2πL

- μ0i√2L
- 4μ0i√5πL

- Zero

**Q.**

Find the magnetic field B at the center of a rectangular loop of length l and width b, carrying a current i.

**Q.**A wire is bent in the form of a circular arc with a straight portion AB. Magnetic field at O when current I is flowing in the wire is

- μ0I2r(π−θ+tanθ)
- μ0I2πr(π+θ−tanθ)
- μ0I2πr(π−θ+tanθ)
- μ0I2πr(−tanθ+π−θ)

**Q.**The magnetic field at the origin due to the current flowing in the wire is

- μ0I8πa(−^i+^k)
- μ0I8πa(^i+^k)
- μ0I2πa(^i+^k)
- μ0I4πa√2(^i−^k)

**Q.**Currents i and 3i are flowing in opposite directions in two co-axial long thin walled circular cylinders of radii a and 2a respectively as shown. Choose correct options. (Length of the cylinder is L)

- Pressure on inner cylinder wall is zero.
- Pressure on inner cylinder wall is μ0i28π2a2.
- Pressure on outer cylinder wall is 3μ0i232 π2a2.
- Force on unit length of outer cylinder is 34μ0i2π a.

**Q.**Shown in the figure, is a conductor carrying current I. The net magnetic induction at the point O is -

[Point O is the common center of all the three arcs.]

- Zero
- μ0Iθ24πR
- 11μ0Iθ24πR
- 5μ0Iθ24πR

**Q.**Figure shows a square loop ABCD with edge length a. The resistance of the wire ABC is r and that of ADC is 2r. The value of magnetic field at the centre of the loop assuming uniform wire is

- √2μ0i3πa⊗

- √2μ0i3πa⊙

- √2μ0iπa⊙

- √2μ0iπa⊗

**Q.**Figure shows an equilateral triangular frame of side L. Frame starts entering into the region of uniform magnetic field B with constant velocity v. If i is instantaneous current through the frame, then the correct graph is. Take anticlockwise current direction to be positive.

**Q.**Current i flows through a long conducting wire bent at right angle as shown in figure. The magnetic field at a point P on the right bisector of the angle XOY at a distance r from O is

- 2μ0iπr

- μ0i4πr(√2+1)

- μ04π.2ir(√2+1)
- μ0iπr

**Q.**A closed circuit is in the form of a regular hexagon of side a. If the circuit carries current I, What is magnetic induction at the cetre of the hexagon?

- √3μ0iπa
- √3μ0iπa
- zero
- None

**Q.**Statement A : A current carrying wire is placed parallel to the external magnetic field. The force on it due to the external magnetic field is zero.

Statement R : The net charge on current wire is zero.

- Both A and R are true, and R is the correct explanation of A.
- Both A and R are true but R is not correct explanation of A.
- A is true, but R is false.
- A is false, but R is true.

**Q.**

A current I flows in a long thin walled cylinder of radius R. What pressure do the walls of the cylinder experience?

μ0I8πR

μ0I28π2R2

μ0I216πR2

μ0I4π2R

**Q.**A point charge of magnitude q = 4.5 nC is moving with speed v = 3.6×107 m/s parallel to the x-axis along the line y = 3 m. Find the magnetic field at the origin produced by this charge when the charge is at the point x = -4 m, y = 3 m, as shown in the figure.

- −3.89×10−10^k T
- 3.89×10−10^i T
- 3.89×10−10^j T
- 3.89×10−10^k T

**Q.**Three circular coils each having two turns and radius R are placed mutually perpendicular to each other and each having its centre at the origin of the coordinate system. If current i is flowing through each coil, then the magnitude of the magnetic field at the common centre is:

- √3μ0iR
- Zero
- √2−1μ0i2R
- (√3−√2)μ0i2R

**Q.**Determine the magnitude of magnetic field at the center (P) of a regular hexagon shaped current loop of side L.

- √3μ0iπL
- 3√3μ0iπL
- 3μ0iπL
- μ0i3πL

**Q.**In a certain region, uniform electric field exists as →E=E0^j. A proton and an electron are projected from origin at time t=0 with certain velocities along +x-axis direction. Due to the electric field, they experience force and move in the xy-plane along different trajectories.

(i) The path followed by the particles will be a

- parabola
- circular
- hyperbola
- spiral

**Q.**A charge of 3.14×10−6 C is distributed uniformly over a circular ring of radius 20 cm. The ring rotates about its axis with angular velocity of 60 rad/s. Find the ratio of electric field to the magnetic field at a point on the axis located at a distance of 5 cm from centre.

- 1.88×1015 m/s
- 2.50×1015 m/s
- 3.20×1015 m/s
- 4.50×1015 m/s

**Q.**

Figure (35-E4) shows a long wire bent at the middle to form a right angle.Show that the magnitudes of the magnetic fields at the points P, Q, R and S are equal and find this magnitude.

**Q.**A wire carrying current i has the configuration as shown in the figure. Two semi-infinite straight sections, each tangent to the same circle, are connected by a circular arc, of angle θ, along the circumference of the circle, with all sections lying in the same plane. What must θ( in rad) be in order for B to be zero at the center of circle is

**Q.**If the magnetic field at ‘P’ can be written as K tan(α2), then K is

- μ0I4πd
- μ0I2πd
- μ0Iπd
- 2μ0I4πd

**Q.**A uniform but time varying magnetic field B=2t3+24t T is present in a cylindrical region of radius R=2.5 cm as shown.

The force on an electron at P at t=2 sec. is

- 48×10−21N
- 24×10−21N
- Zero
- 96×10−21N

**Q.**

Figure (35-E6) shows a square loop of edge a made of a uniform wire.A current i enters the loop at the point A and leaves it at the point C.Find the magnetic field at the point P which is on the perpendicular bisector of AB at a distance a/4 from it.

**Q.**

Consider a straight piece of length x of a wire carrying a current i.Let P be a point on the perpendicular bisector of the piece, situated at a distance d from its middle point.Show that for d>>x, the magnetic field at P varies as 1/d2 whereas d<<x, it varies as 1/d.

**Q.**Earths magnetic field at a place where angle of dip is 37 degree and vertical component of Earths magnet is 0.5 G is

**Q.**Figure shows an infinitely long current carrying wire bent at an angle α. The magnetic induction at the point P located on the angle bisector at a distance x from the point O at the bend is given by μ0I2πxcotαn. The value of n is

**Q.**a particle moving towards east enters a magntic field directed towards north and deflected towards vertically downward direction . the charged particled is?