Exams › JEE Advanced › Physics

A wire shaped as one full cycle of a sine curve lies in the x-y plane and is moved with velocity V = Vx i + Vy j. A magnetic field B = -B0 k exists in the region. Find the motional EMF developed between the two ends P and Q of the wire.

1. B0*Vx times the vertical separation between P and Q
2. B0*Vy times the horizontal separation between P and Q
3. B0*(Vx + Vy)
4. 0

Correct answer: B0*Vx times the vertical separation between P and Q

Solution

For a wire in a uniform field, the motional EMF depends only on the straight vector L joining the endpoints: EMF = (V x B).L. With B = -B0 k and V = Vx i + Vy j, V x B = (Vx i + Vy j) x (-B0 k) = -B0*Vx (i x k) - B0*Vy (j x k) = -B0*Vx(-j) - B0*Vy(i) = B0*Vx j - B0*Vy i. Taking the dot product with the end-to-end vector L, only the component of L along the resultant survives. For the standard configuration the net EMF equals B0*Vx multiplied by the vertical (y-direction) separation between P and Q. Hence the answer is B0*Vx times the vertical separation between the endpoints.

Related JEE Advanced Physics questions

• What is the final velocity attained by the loop?
• A long coaxial cable is made up of two cylindrical conductors with radii a and b. The inner conductor carries a constant current i, while the outer conductor acts as the return path for the current. What is the self-inductance of a segment of the cable of length l?
• Determine the inductance per unit length for a loop created by connecting the ends of two infinitely long parallel wires, each with radius r, and separated by a distance d between their centers. Ignore the magnetic flux inside the wires and the effects at the ends.
• If the electromotive force is 10 V and the rate of change of current is calculated as 2.5 A/s, what is the self-inductance of the coil, given by L = e / (dl/dt)?
• The magnitude of the induced electric field in the orbit at any instant of time during the time interval of the magnetic field change is
• A semicircular loop of radius r is positioned on the axis of a large current-carrying circular ring of radius R (with R >> r). The loop is placed at an axial distance of R*sqrt(3) from the center of the ring, and the plane of the semicircular loop makes an angle of 53 deg with the plane of the ring. Find the mutual inductance M between the two coils.

⚔️ Practice JEE Advanced Physics free + battle 1v1 →