Question

Consider the given case
Magnetic field of 1 tesla is applied to the arrangement. If connecting wires and rods have negligible resistance. Then, current through $5\Omega $resistance is

A. 120mA
B. 40mA
C. 80mA
D. 60mA

Answer 1

Hint: As a very first step, one could read the question well and hence note down the given values from the figure as well as the question. Then, one could recall the concept of motional emf and also the formula and find the motional emf produced by the two rods. From that you will get the potential difference across the resistor. Using Ohm’s law you will get the answer.

Formula used:
Motional emf,
E=Blv

Complete step by step solution:
In the question, we are given an arrangement where we have two rods of negligible resistance and a resistor of resistance $5\Omega $that are connected through wires of negligible resistance and this whole setup is placed under a magnetic field of 1Tesla. We are supposed to find the current through the given resistor. The concept that we have to use here is the concept of motional emf.
Let us first find the motional emf produced in the rod AB,
${{E}_{AB}}=Blv$
$\Rightarrow {{E}_{AB}}=1\times 0.1\times 4=0.4V$……………………………………….. (1)
Now for the rod CD we have,
${{E}_{CD}}=Blv$
$\Rightarrow {{E}_{CD}}=1\times 0.1\times 2=0.2V$
Now the whole arrangement would appear to be equivalent to the circuit given below,

Now we have the potential difference across the given resistor to be,
$V={{E}_{AB}}-{{E}_{CD}}=0.4-0.2=0.2V$
Now let us recall the Ohm’s law that is given by,
$V=IR$
$\Rightarrow I=\dfrac{V}{R}$
Substituting the given values we get,
$I=\dfrac{0.2}{5}=0.04A$
$\therefore I=40mA$
Therefore, we found the current through the resistor to be equal to 40mA. Hence, option B is the correct answer.

Note: You may be familiar with the fact that any change in magnetic flux would induce an emf opposing this change by the method of induction. Motion can be one of the causes of this induction. The emf induced as the result of motion in a magnetic field is what we call the motional emf.