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
Predict the polarity of the capacitor in the situation described below :
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
A short bar magnet placed with its axis at 30° with a uniform external magnetic field of 0.25 T experiences a torque of magnitude equal to 4.5 × 10–2 J. What is the magnitude of magnetic moment of the magnet?
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 statements about bar magnet is correct?
When iron filings are sprinkled on a sheet of glass placed over a short bar magnet then, the iron filings form a pattern suggesting that the magnet has ______.
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?
According to the dipole analogy 1/ε0 corresponds to ______.
Four point masses, each of value m, are placed at the comers of a square ABCD of side L, the moment of inertia of this system about an axis through A and parallel to BD is ______.
When a current is passed through a tangent galvanometer, it gives a deflection of 30° for 60° correction, the current must be
A magnetic needle suspended freely orients itself:-
A particle having charge 100 times that of an electron is revolving in a circular path by radius 0.8 with one rotation per second. The magnetic field produced at the centre is
A bar magnet of magnetic moment 3.0 Am is placed in a uniform magnetic field of 2 × 10-5T. If each pole of the magnet experience a force of 6 × 10-4 N, the length of the magnet is ______.
Magnetic dipole moment is a ______
A proton has spin and magnetic moment just like an electron. Why then its effect is neglected in magnetism of materials?
A ball of superconducting material is dipped in liquid nitrogen and placed near a bar magnet. (i) In which direction will it move? (ii) What will be the direction of it’s magnetic moment?
Suppose we want to verify the analogy between electrostatic and magnetostatic by an explicit experiment. Consider the motion of (i) electric dipole p in an electrostatic field E and (ii) magnetic dipole m in a magnetic field B. Write down a set of conditions on E, B, p, m so that the two motions are verified to be identical. (Assume identical initial conditions.)
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?
A bar magnet is demagnetized by inserting it inside a solenoid of length 0.2 m, 100 turns, and carrying a current of 5.2 A. The coercivity of the bar magnet is ______.
