Science (English Medium) कक्षा १२ - CBSE Question Bank Solutions

Consider a solid sphere of radius r and mass m that has a charge q distributed uniformly over its volume. The sphere is rotated about its diameter with an angular speed ω. Show that the magnetic moment µ and the angular momentum l of the sphere are related as `mu = q/(2m) l`

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 for d << x, it varies as 1/d.  

The wire ABC shown in figure forms an equilateral triangle. Find the magnetic field B at the centre O of the triangle assuming the wire to be uniform. 

Figure shows a part of an electric circuit. The wires AB, CD and EF are long and have identical resistance. The  separation between the neighbouring wires is 1.0 cm. The wires AE and BF have negligible resistance and the ammeter reads 30 A. Calculate the magnetic force per unit length of AB and CD. 

A long, straight wire is fixed horizontally and carries a current of 50.0 A. A second wire having linear mass density 1.0 × 10⁻⁴ kg m⁻¹ is placed parallel to and directly above this wire at a separation of 5.0 mm. What current should this second wire carry such that the magnetic repulsion can balance its weight? 

Consider the situation shown in the figure. Suppose the circular loop lies in a vertical plane. The rod has a mass m. The rod and the loop have negligible resistances but the wire connecting O and C has a resistance R. The rod is made to rotate with a uniform angular velocity ω in the clockwise direction by applying a force at the midpoint of OA in a direction perpendicular to it. Find the magnitude of this force when the rod makes an angle θ with the vertical.

In the circuit shown in the figure, find the value of the current shown in the ammeter A.

A screen is placed 80 cm from an object. The image of the object on the screen is formed by a convex lens placed between them at two different locations separated by a distance 20 cm. determine the focal length of the lens.

A straight horizontal conducting rod of length 0.45 m and mass 60 g is suspended by two vertical wires at its ends. A current of 5.0 A is set up in the rod through the wires.

(a) What magnetic field should be set up normal to the conductor in order that the tension in the wires is zero?

(b) What will be the total tension in the wires if the direction of current is reversed keeping the magnetic field same as before?
(Ignore the mass of the wires) g = 9.8 m s^–2.

Correct expression for force on a current carrying conductor of length dl in a magnetic field is ______.

Thin lens approximation for a lens is ______.

An electron is projected with uniform velocity along the axis of a current carrying long solenoid. Which of the following is true?

When a magnetic compass needle is carried nearby to a straight wire carrying current, then

1. the straight wire cause a noticeable deflection in the compass needle.
2. the alignment of the needle is tangential to an imaginary circle with straight wire as its centre and has a plane perpendicular to the wire.

A charged particle is moving on circular path with velocity v in a uniform magnetic field B, if the velocity of the charged particle is doubled and strength of magnetic field is halved, then radius becomes ______.

A small object with charge q and weight mg is attached to one end of a string of length ‘L’ attached to a stationary support. The system is placed in a uniform horizontal electric field ‘E’, as shown in the accompanying figure. In the presence of the field, the string makes a constant angle θ with the vertical. The sign and magnitude of q ______.