Question

An arbitrary shaped closed coil is made of a wire of length L and a current I ampere is flowing in it. If the plane of the coil is perpendicular to magnitude field B, the force on the coil is?
A. Zero
B. IBL
C. 2IBL
D. 1/2 IBL

Answer 1

Hint: In this question an arbitrary shaped closed coil is placed in the magnetic field (perpendicular to each other). The coil carries a current of amount I and the length of wire is L. As we placed the coil in the magnetic field, the coil will experience a force which is magnetic force in the direction perpendicular to current and magnetic field direction. We can determine the direction of magnetic force by Fleming’s left hand rule.

Formula used:
In a magnetic field, moving charges constantly experience force. The vector quantity for this force is given as:
$F=i(l\times B)$
In this equation, F stands for force, I for current flowing through the conductor, l for conductor length, and B for magnetic field. This vector notation can be further condensed to, $F=iBl \sin \theta$ where $\theta$ denotes the angle between the magnetic field and the elemental current length.

Complete step by step solution:
The earth's inherent magnetic shields it from solar radiation from the sun. Additionally, it offers a field of operation for a magnetic compass. While electromagnets are coils that create the magnetic field when an electric current flows through them, permanent magnets have their own intrinsic magnetism and are made of ferromagnetic materials like iron, nickel, or alnico alloys.

For instance, a current-carrying conductor creates a magnetic field around it. The strength of the field can be adjusted in accordance with the amount of current flowing through the conductor around the coil, and the field's direction is governed by the Right-Hand Screw Rule.

Electromagnets are used in a variety of sectors for different manufacturing and production operations. Both a North pole and a South pole exist in the magnetic field. In contrast to an electric field, where a charge can be separated, a monopole does not exist for a magnetic field.

As discussed in a hint that when both magnetic field and current carrying coil is placed perpendicular to each other, the direction of magnetic force experienced by the coil can be determined by the left hand Fleming's rule.

According to Fleming left hand rule when we place out forefinger in the direction of magnetic field and middle finger in the direction current, then the direction of thumb will indicate the direction of motion of magnetic force such as,


As the electric field is entering the coil and lets say current in clockwise direction so align your left hand middle finger in the direction of current and fore finger in the direction of magnetic field (both perpendicular to each other). On left side of coil you will see thumb pointing upward and when you check the same on right side of coil, totally opposite, the thumb direction will in downward direction.

Thus we can say that on the left side the amount of force acting upward is the same as the amount of force applied on the right side but in the opposite direction, so the net force acting one the coil is zero.

Hence, option A is correct.

Note: As per question the angle between magnetic field and current in the coil or coil plane is of ninety degree (perpendicular) due to which sin component is used in the formula. Now, when we determine the cross product of current (let say i vector) and magnetic field (let say J vector) we will get magnetic force (K vector) which will be again perpendicular to both magnetic field and current direction.