A copper wire bent in the shape of a semicircle of radius r translates in its plane with a constant velocity v. A uniform magnetic field B exists in the direction perpendicular to the plane of the wire. Find the emf induced between the ends of the wire if (a) the velocity is perpendicular to the diameter joining free ends, (b) the velocity is parallel to this diameter.

Open in App

Solution

(a) The emf induced between the ends of the wire is calculated using the following formula:
e = Bv (Effective length of the wire)
Effective length of the wire = Component of length perpendicular to the velocity
Here, the component of length moving perpendicular to v is 2r.
∴ Induced emf, e = Bv2r

(b) When the velocity is parallel to the diameter of the semicircular wire, the component of its length perpendicular to its velocity is zero.
∴ Induced emf, e = 0

Suggest Corrections

Similar questions

A copper wire bent in the shape of a semicircle of radius r translates in its plane with a constant velocity v. A uniform magnetic field B exists in the direction perpendicular to the ends of the wire if

(a) The velocity is perpendicular to the diameter joining free ends,

(b) The velocity is parallel to this diamneter.

Q. A copper wire of length lis bent into a semicircle. It is moved with a velocity v in a region where magnetic field is uniform and perpendicular to the plane of the wire. If the strength of the field is B then emf induced

Q. A semicircular wire of radius

R

is rotated with constant angular velocity about an axis passing through one end and perpendicular to the plane of the wire. There is a uniform magnetic field of strength

B

. The induced emf between the ends is

Q. A metallic wire bent in form of a semi-circle of radius 0.1 m is moved in a direction parallel to its plane, but perpendicular to a magnetic field

B = 20

mT with a velocity of 10 m/s. What is the induced e.m.f. in wire?

Q. A circular copper-ring of radius r translates in its plane with a constant velocity v. A uniform magnetic field B exists in the space in a direction perpendicular to the plane of the ring. Consider different pairs of diametrically opposite points on the ring. (a) Between which pair of points is the emf maximum? What is the value of this maximum emf? (b) Between which pair of points is the emf minimum? What is the value of this minimum emf ?

Join BYJU'S Learning Program