1.0 m rectangular loop with a sliding connector is in uniform magnetic field 2t perpendicular to plane of loop. Resistance is 2 ohms. Two resistances, 6 ohms and 3 ohms, are connected.

Now, as per the question, the external force needed to keep connector moving with constant velocity equals 2ms−1. With the given data, we have to determine force.

Accoding to the question, the following can be said:

  • Resistance of Connector = 2Ω
  • Given Magnetic Field = 2t
  • Other Two Resistances = 6Ω and 3Ω (velocity of moving connector is 2ms−1)

Now, in order to estimate the induced emf generated in the circuit, E = vBl

⇒ E = 2 × 2 × 1

⇒ E = 4V

Thus, after assuming the two resistances 6Ω and 3Ω because they’re parallelly connected, then the resultant resistance should be 2Ω.

Therefore, the value of I (current) that flows via the circuit is, I = 4/2 + 2, giving the value of 1 Ampere (flowing in a clockwise direction). Now, in order to estimate the magnetic force on the connector by using the formula:

F = ilB

After replacing the values, we get,

F = 1 × 1 × 2

⇒ F = 2N, (Thus, the direction of force is towards left).

Thus, it can be said that if we want to move our connector with a constant velocity, a force of 2N is needed to be applied.


Related Questions

  1. For The Resistor Combination, Find The Equivalent Resistance Between M and N.
  2. A Circuit Consists Of A Battery Of 3 Cells (2 V Each), A Combination Of Three Resistors, 10 Ohm, 20 Ohm And 30 Ohm, Attached Parallelly, With Plug Key And Ammeter (In Series).
  3. Three Incandescent Bulbs (Each 100 W) Are Attached In Series. In Another Circuit, Three More Bulbs Of Same Wattage Are Attached Parallelly To An Equal Source.
  4. Two Identical Resistors With Resistances 15 Ohm Are Connected In Series And Parallel To A Battery Of 6 V. Calculate Ratio Of Power Consumed.
  5. In An Arrangement Of Resistances, Find Effective Resistance Between Points A and B.
  6. What Is Effective Resistance?
  7. Draw An Electric Circuit With A Cell, Key, Ammeter, A Resistor (Series) Of 2 Ohm With a Combination Of Two Resistors (4 Ohm Each) In Parallel And A Voltmeter Across a Parallel Combination.
  8. Find The Highest And Lowest Total Resistance Of A Combination Of Four Coils With Resistances 4 Ohms, 8 Ohms, 12 Ohms, 24 Ohms.
  9. What is Null Voltage?
  10. X and Y, which are two resistors, with resistances of 2 Ω and 3 Ω respectively are first connected in parallel and then in series. In both cases, the voltage that is supplied is 5 V. (i) Illustrate a circuit diagram to show the combination of resistors. (ii) Calculate the amount of voltage across 3 Ω resistor in the series combination of resistors.
  11. If R, C And L Are Fundamental Quantities In A Circuit Like Resistance, Capacitance And Inductance In W, Then Find Dimensional Formula For Resistance And Capacitance.

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CBSE CLASS XII Related Questions

  • 1.
    A charged particle $+q$ in an electric field $\vec{E}$ experiences a force in the direction of the electric field. As a result, its kinetic energy changes. Similarly, the charged particle also experiences a force when it moves in a magnetic field $\vec{B}$. But this magnetic force is perpendicular to both velocity $\vec{v}$ of the charged particle and the magnetic field $\vec{B}$, so it cannot change the kinetic energy of the charged particle. Consider two charged particles 1 and 2 of masses $m$ and $\frac{m}{2}$ having charges $-q$ and $+2q$ respectively. They are accelerated from rest through the same potential difference $V$ and acquire kinetic energy $K_1$ and $K_2$. Then they enter in a region of uniform magnetic field $\vec{B}$ perpendicular to their velocities.


      • 2.
        With the help of a labelled diagram, explain the principle, construction and working of an a.c. generator.


          • 3.
            Two metal spheres of radii $r_1$ and $r_2$ ($> r_1$) having charges $q_1$ and $q_2$ respectively kept in air, are brought in contact. Which of the following statements is not correct ?

              • The total charge of the two spheres is conserved.
              • Both spheres attain the same potential.
              • The final potential of the system equals $\frac{1}{4\pi\epsilon_0} \frac{(q_1 + q_2)}{(r_1 + r_2)}$
              • The final potential of the system equals $\frac{1}{4\pi\epsilon_0} \frac{(q_1 + q_2) (r_1 + r_2)}{r_1 r_2}$

            • 4.
              An electric field $\vec{E}$ is established across the ends of a cylindrical conductor of length L and area of cross-section A. Discuss how electrons attain an average velocity, independent of time. Hence, obtain a relation between current in the conductor and this ‘average velocity’ of electrons.


                • 5.
                  Capacitors are manufactured with certain standard capacitances and working voltages. However, these standard values may not be the ones that are actually needed in a particular application. Two or more capacitors can be grouped in series or in parallel to achieve desired capacitance and voltage. When connected in series, the total capacitance decreases while the voltage rating increases, whereas in parallel connections, the total capacitance increases and maintains the same voltage rating. A capacitor stores energy in the electric field between its plates and stored energy is proportional to the square of the voltage and capacitance $U = \frac{1}{2}CV^2$, where symbols have their usual meanings.
                  Two capacitors, one of $3 \ \mu$F and the other of $6 \ \mu$F, are connected in series in the circuit as shown in the figure, for a long time. }


                    • 6.
                      Read the following paragraph and answer the questions that follow.
                      In an experiment with convex lens of focal length f, the screen is fixed at a distance D from the object. A student slowly moves the lens away from the object towards the screen and finds that she is able to form sharp image of the object for two positions of the lens. The distance between these two positions of the lens is d.

                        CBSE CLASS XII Previous Year Papers

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