Question

(a) Define one tesla.
(b) Derive an expression for force experienced by a current carrying straight conductor placed in a magnetic field. How can we find the direction of force?

Answer 1

To define one tesla, refer to the formula for magnetic force on the moving charge. To derive the expression for force experienced by a current carrying straight conductor placed in a magnetic field, recall the expression for the magnetic force acting on the moving charge in the magnetic field.

Formula used:
The magnetic force acting on the charged particle moving in the magnetic field B is,
$F = qvB\sin \theta$
Here, q is the charge, v is the velocity and the angle between the velocity vector of the charge and magnetic field vector is $\theta$.

Complete step by step answer:
(a) We know that tesla is the S.I unit of magnetic field. The magnetic field is said to be one tesla if 1 C charge moving with velocity 1 m/s perpendicular to the direction of magnetic field experiences a force of 1 N.

(b) We assume the charge q is flowing through a straight conductor with velocity v. The straight conductor is placed in the magnetic field of magnitude B. We assume the angle between the velocity vector of the charge and the magnetic field vector is $\theta$.
We know that the magnetic force acting on the charged particle placed in the uniform magnetic field B is expressed as,
$F = qvB\sin \theta$ …… (1)
Here, q is the magnitude of the charge and v is the magnitude of the velocity.
We know that the current flowing through the conductor is the ratio of charge per unit time. Therefore,
$I = \dfrac{q}{t}$
$\Rightarrow q = It$
Therefore, we can rewrite equation (1) as follows,
$F = \left( {It} \right)vB\sin \theta$
But we know that the product of velocity and time is the displacement of the charge which is equal to the total length of the conductor. Therefore, we can write,
$F = I\,L\,B\sin \theta$
$\therefore F = I\left( {L \times B} \right)$

This is the expression for force experienced by the current carrying straight conductor when placed in the magnetic field.
We can find the direction of magnetic force using Fleming’s left hand rule which states that if we hold the charged conductor in our left hand such that the forefinger points in the direction of magnetic field and the middle finger points the direction of current then the direction of thumb represents the direction of magnetic force.

Note: To define one tesla, we have referred to equation (1) by rearranging it for the magnetic field B. Always remember, the current is the rate of flow of charges per unit time and not the product of charge and time. To determine the direction of the magnetic field, students should always use the left hand and not the right hand.