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Chapter 23: Q23PE (page 861)

Derive an expression for the current in a system like that in figure below, under the following conditions. The resistance between the rails is R , the rails and the moving rod are identical in cross section A and have the same resistivity 蚁. The distance between the rails is l, and the rod moves at constant speed v perpendicular to the uniform field B. At time zero, the moving rod is next to the resistance R.

Short Answer

Expert verified

The expression isIt=ABLvAR+蚁L+vt

Step by step solution

01

Step 1:Definition of Lenz’s law

According to Lenz, the direction of induced emf and hence the direction of the induced current is such that it will oppose the motion of the conductor in the external field.

02

Deriving the equation for intensity

The current (I) can be calculated using Ohm's law, as-

I(t)=蔚tR(t)

Where 蔚is emf and R is Resistance.

The emf 蔚will be given as

蔚t=BLv

The resistance (R) of the metal structure, which means,

Rt=R+蚁L+vtA

Combining the two expressions, we get,

I(t)=BLvR+蚁L+vtA

The above equation can further be expressed as-

It=ABLvAR+蚁L+vt

This is the required expression.

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