Advertisements
Advertisements
प्रश्न
Solve the following problem.
Two small and similar bar magnets have a magnetic dipole moment of 1.0 Am2 each. They are kept in a plane in such a way that their axes are perpendicular to each other. A line drawn through the axis of one magnet passes through the center of other magnet. If the distance between their centers is 2 m, find the magnitude of the magnetic field at the midpoint of the line joining their centers.
Advertisements
उत्तर
Let P be the midpoint of the line joining the centres of two bar magnets. As shown in figure, P is at the axis of one bar magnet and at the equator of another bar magnet. Thus, the magnetic field on the axis of the first bar magnet at distance of 1 m from the centre will be,
Ba = `μ_0/(4π)(2"m")/"r"^3`
= `10^-7xx(2xx1.0)/(1)^3`
= 2 × 10−7 Wb/m2
Magnetic field on the equator of second bar magnet will be,
Beq = `μ_0/(4π)("m")/"r"^3`
= `10^-7xx1.0/(1)^3`
= 1 × 10−7 Wb/m2
The net magnetic field at P,
Bnet = `sqrt("B"_"a"^2+"B"_"eq"^2)`
= `sqrt((2xx10^-7)^2+(1xx10^-7)^2)`
= `sqrt((10^-7)^2xx(4+1))`
= `sqrt(5)xx10^-7` Wb/m2
Magnitude of net magnetic field at midpoint of line will be `sqrt(5)xx10^-7` Wb/m2.
APPEARS IN
संबंधित प्रश्न
Write any three properties of magnetic lines of force.
How are the magnetic field lines different from the electrostatic field lines?
A bar magnet of length 1 cm and cross-sectional area 1.0 cm2 produces a magnetic field of 1.5 × 10−4 T at a point in end-on position at a distance 15 cm away from the centre. (a) Find the magnetic moment M of the magnet. (b) Find the magnetisation I of the magnet. (c) Find the magnetic field B at the centre of the magnet.
Answer the following question.
Write the four important properties of the magnetic field lines due to a bar magnet.
An electron moves along +x direction. It enters into a region of uniform magnetic field `vec B` directed along −z direction as shown in fig. Draw the shape of the trajectory followed by the electron after entering the field.
Choose the correct option.
Inside a bar magnet, the magnetic field lines
Answer the following question in brief.
What happens if a bar magnet is cut into two pieces transverse to its length/along its length?
Solve the following problem.
A magnetic pole of a bar magnet with a pole strength of 100 A m is 20 cm away from the centre of a bar magnet. The bar magnet has a pole strength of 200 A m and has a length of 5 cm. If the magnetic pole is on the axis of the bar magnet, find the force on the magnetic pole.
Answer the following question in detail.
A circular magnet is made with its north pole at the centre, separated from the surrounding circular south pole by an air gap. Draw the magnetic field lines in the gap.
Answer the following question in detail.
Two bar magnets are placed on a horizontal surface. Draw magnetic lines around them. Mark the position of any neutral points (points where there is no resultant magnetic field) on your diagram.
A closely wound solenoid of 800 turns and area of cross-section 2.5 × 10–4 m2 carries a current of 3.0 A. Explain the sense in which the solenoid acts like a bar magnet. What is its associated magnetic moment?
A closely wound solenoid of 2000 turns and area of cross-section 1.6 × 10–4 m2, carrying a current of 4.0 A, is suspended through its centre allowing it to turn in a horizontal plane.
- What is the magnetic moment associated with the solenoid?
- What is the force and torque on the solenoid if a uniform horizontal magnetic field of 7.5 × 10–2 T is set up at an angle of 30° with the axis of the solenoid?
A closely wound solenoid of 2000 turns and area of cross-section 1.6 × 10-4 m2 , carrying a current of 4.0 A, is suspended through its centre allowing it to turn in a horizontal plane.
What is the force and torque on the solenoid if a uniform horizontal magnetic field of 7.5 × 10-2 T is set up at an angle of 30° with the axis of the solenoid?
Which of the following statement about magnetic field lines is true?
In which case of comparing solenoid and bar magnet there is no exact similarity?
Magnetic field at far axial point due to solenoid as well as bar magnet varies ______.
Magnetic moment for solenoid and corresponding bar magnet is ______.
A magnetic needle suspended freely orients itself:-
Magnetic dipole moment is a ______
A bar magnet of magnetic moment m and moment of inertia I (about centre, perpendicular to length) is cut into two equal pieces, perpendicular to length. Let T be the period of oscillations of the original magnet about an axis through the midpoint, perpendicular to length, in a magnetic field B. What would be the similar period T′ for each piece?
Verify the Ampere’s law for magnetic field of a point dipole of dipole moment m = m`hatk`. Take C as the closed curve running clockwise along (i) the z-axis from z = a > 0 to z = R; (ii) along the quarter circle of radius R and centre at the origin, in the first quadrant of x-z plane; (iii) along the x-axis from x = R to x = a, and (iv) along the quarter circle of radius a and centre at the origin in the first quadrant of x-z plane.
There are two current carrying planar coils made each from identical wires of length L. C1 is circular (radius R) and C2 is square (side a). They are so constructed that they have same frequency of oscillation when they are placed in the same uniform B and carry the same current. Find a in terms of R.
