Question

If a wire of length 1 meter placed in uniform magnetic field 1.5 tesla at angle $30{}^\circ$ with magnetic field. The current in a wire is 10 amp. Then force on a wire will be
A. 7.5 N
B. 1.5 N
C. 0.5 N
D. 2.5 N

Answer 1

Hint: To solve this question, we need to remember the concept of force applied on a current carrying conductor when it’s put in a magnetic field. We need to know the formula of force experienced by the wire which is carrying a current when it’s put in the magnetic field.

Formula used:
\[\vec{F}=i(\vec{l}\times \vec{B})\]
In this equation, F stands for force, I for current flowing through the conductor, l for conductor length, and B for magnetic field.

Complete step by step solution:
The direction of the force experienced by the wire can be determined by the Fleming's left hand rule. The procedure to find the direction of the force by the Fleming’s left hand rule is as follows:
Keeping our left hand's thumb, forefinger, and middle finger at right angles to one another. The thumb will point in the direction of the force acting on the current carrying conductor, and the forefinger and middle finger of the left hand should point in the direction of the external magnetic field and the current flowing in the conductor, respectively, in accordance with the above diagram.

Now according to the question we need to find the force applied on the wire. So, we will use the formula:
$F=Bil\sin \theta$
So by putting all the values, i= 10 amp, l=1 meter and the angle = $30{}^\circ$ we get
\[F=1.5\times 1\times 10\times \sin 30{}^\circ \]
$\therefore F=\dfrac{15}{2}=7.5\,N$

Hence, option A is correct.

Additional information: In the vicinity of a magnet, an electric current, or a shifting electric field, there is a vector field called a magnetic field where magnetic forces can be seen. Electric charges in motion and the intrinsic magnetic moments of elementary particles connected to the fundamental quantum characteristic known as spin create a magnetic field. As parts of the electromagnetic force, one of the four fundamental forces of nature, magnetic field and electric field are interdependent. Typically, there are two ways to depict a magnetic field.
-Magnetic Field Lines
-Magnetic Field Vector

Magnetic Field Lines: A visual representation of magnetic fields is made using magnetic field lines. They explain the direction of the magnetic force acting on a north monopole at each particular location.

Magnetic Field Vector: Mathematically, the magnetic field can be represented as a vector field. A grid-drawn collection of several vectors is known as a vector field. Each vector in this situation has a length that depends on the strength of the magnetic field and points in the same general direction as a compass would.

Note: The magnetic field and the elemental current length are both perpendicular to the direction of the force that the current-carrying conductor feels when it is put in a magnetic field. The current flows in the same direction as the length of the elemental current. We use the conductor's elemental current length in the formula by convention.